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main.js
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main.js
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createExerciseButtonBox();
createExerciseBox();
createRootEnvironment();
createFormulaWindow();
createDeductionsBox();
createProofBox();
createTermWindow();
createAchievementsBox();
createNotificationsBox();
createOperatorsWindow();
createUndoButton();
createRestartButton();
createPrevExerciseButtons();
createNextExerciseButtons();
createResetButton();
createEditStateButton();
document.body.setAttribute("onkeydown", "keydown(event)");
// A mapping from law shortName to the pair [givens, conclusion].
var lawsData = {
"LawConjunction1": [[A, B], AND(A,B)],
"LawConjunction2": [[AND(A,B)], A],
"LawConjunction3": [[AND(A,B)], B],
"LawDisjunction1": [[formulaContext(B), A], OR(A,B)],
"LawDisjunction2": [[formulaContext(B), A], OR(B,A)],
"LawAssumption": [[formulaContext(A)], assuming(A,A)],
"And": [[formulaContext(A), formulaContext(B)], formulaContext(AND(A,B))],
"Or": [[formulaContext(A), formulaContext(B)], formulaContext(OR(A,B))],
"Implies": [[formulaContext(A), formulaContext(B)], formulaContext(IMPLIES(A,B))],
"LawImplication": [[assuming(B,A), rootEnvironmentContext()], IMPLIES(A,B)],
"Push": [[A, environmentContext([B])], assuming(A,B)],
"PushAlt": [[A, formulaContext(B)], assuming(A,B)],
"ModusPonens": [[A, IMPLIES(A,B)], B],
"CaseAnalysis": [[assuming(C,A), assuming(C,B)], assuming(C,OR(A,B))],
"Iff": [[formulaContext(A), formulaContext(B)], formulaContext(IFF(A,B))],
"BiconditionalIntroduction": [[IMPLIES(A,B), IMPLIES(B,A)], IFF(A,B)],
"BiconditionalElimination1": [[IFF(A,B)], IMPLIES(A,B)],
"BiconditionalElimination2": [[IFF(A,B)], IMPLIES(B,A)],
"Not": [[formulaContext(A)], formulaContext(NOT(A))],
"caseElimination1": [[OR(A,B), NOT(A)], B],
"caseElimination2": [[OR(A,B), NOT(B)], A],
"ExcludedMiddle": [[formulaContext(A)], OR(A,NOT(A))],
"True": [[formulaContext(TRUE())], TRUE()],
"False": [[formulaContext(NOT(FALSE()))], NOT(FALSE())],
"False2": [[formulaContext(FALSE())], NOT(FALSE())],
"PushVar": [[A, x], assuming(A, x)],
"forAll": [[formulaContext(A), toTerm(X)], formulaContext(forAll(A,X))],
"thereExists": [[formulaContext(A), toTerm(X)], formulaContext(thereExists(A,X))],
"PushSet": [[A, settingAssumption(B,x)], assuming(A, settingAssumption(B,x))],
"Pull": [[assuming(A, settingAssumption(B,x))], A],
"Pull2": [[assuming(A, settingAssumption(B,x)), rootEnvironmentContext()], A],
"Existence": [[TRUE(), X], thereExists(TRUE(),X)],
"Existence2": [[formulaContext(TRUE()), X], thereExists(TRUE(),X)],
"Reflexivity": [[alpha], equals(alpha,alpha)],
"UniversalIntroduction": [[assuming(Px,x),toTerm(X)], forAll(PX,X)],
"UniversalIntroduction2": [[assuming(Px,x), rootEnvironmentContext()], forAll(PX,X)],
// TODO: is it necessary for this law's shortName to match the shortName
// of the Exercise it is used to construct? If not, it can be given
// a more natural shortName like UniversalRenamingBoundVar.
"18.1": [[forAll(PX,X)], forAll(PY,Y)],
"UniversalSpecification": [[forAll(PX,X), alpha], Pa],
"UniversalSpecification2": [[forAll(PX,X), toTerm(x)], assuming(Px,x)],
"ExistentialInstantiation": [[thereExists(PX,X), toTerm(x)], assuming(Px, settingAssumption(Px,x))],
"ExistentialInstantiation2": [[thereExists(PX,X)], assuming(Px, settingAssumption(Px,x))],
"ExistentialIntroduction": [[Pa, alpha], thereExists(PX,X)],
"ExistentialIntroduction2": [[Pa, alpha, X], thereExists(PX,X)],
"Indiscernability": [[Pa, equals(alpha,beta)], Pb],
};
var lawElements = getElement("lawContainer").children
for (var i = 0; i < lawElements.length; i++) {
var div = lawElements[i];
var id = div.id;
// An example id is "law-LawConjunction1".
var shortName = id.split("-", 2)[1];
var lawName = div.innerHTML;
var pair = lawsData[shortName];
if (!pair) {
throw new Error("law shortName not found: " + shortName);
}
var givens = pair[0];
var conclusion = pair[1];
new Law(shortName, lawName, givens, conclusion);
}
var universalIntroduction = lawsByShortName["UniversalIntroduction"];
var universalIntroduction2 = lawsByShortName["UniversalIntroduction2"];
var universalRenamingBoundVar = lawsByShortName["18.1"];
var universalSpecification = lawsByShortName["UniversalSpecification"];
var universalSpecification2 = lawsByShortName["UniversalSpecification2"];
var existentialInstantiation = lawsByShortName["ExistentialInstantiation"];
var existentialInstantiation2 = lawsByShortName["ExistentialInstantiation2"];
var existentialIntroduction = lawsByShortName["ExistentialIntroduction"];
var existentialIntroduction2 = lawsByShortName["ExistentialIntroduction2"];
var indiscernability = lawsByShortName["Indiscernability"];
// A mapping from exercise shortName to the pair [givens, conclusion].
var exerciseData = {
"1.1": [[A, B], AND(AND(B,A),B)],
"1.2": [[A], AND(A,A)],
"2.1": [[AND(A,B)], AND(B,A)],
"2.2(a)": [[AND(AND(A,B),C)], AND(A,AND(B,C))],
"2.2(b)": [[AND(A,AND(B,C))], AND(AND(A,B),C)],
"3.1(a)": [[A, formulaContext(B), formulaContext(C)], OR(C,OR(A,B))],
"3.1(b)": [[A], OR(A,A)],
"4.1": [[formulaContext(A)], assuming(AND(A,A),A)],
"5.1": [[formulaContext(A), formulaContext(B), formulaContext(C)], assuming(OR(AND(A,B),C), OR(AND(A,B),C))],
"5.2": [[formulaContext(A), formulaContext(B)], assuming(assuming(A,A),B)],
};
function exerciseFromShortName(shortName) {
var pair = exerciseData[shortName];
if (!pair) {
throw new Error("exercise shortName not found: " + shortName);
}
exerciseFromData(shortName, pair[0], pair[1]);
}
newSection("1", "Conjunction introduction");
["1.1", "1.2"].forEach(exerciseFromShortName);
newSection("2", "Conjunction elimination");
["2.1", "2.2(a)", "2.2(b)"].forEach(exerciseFromShortName);
newSection("3", "Disjunction introduction");
["3.1(a)", "3.1(b)"].forEach(exerciseFromShortName);
newSection("4", "Assumption");
["4.1"].forEach(exerciseFromShortName);
newSection("5", "Logical connectives");
["5.1", "5.2"].forEach(exerciseFromShortName);
newSection("6", "Deduction theorem");
exerciseFromData("6.1(a)", [formulaContext(A)], IMPLIES(A,A));
exerciseFromData("6.1(b)", [formulaContext(A), formulaContext(B)], IMPLIES(AND(A,OR(A,B)),A));
exerciseFromData("6.2", [assuming(assuming(C,B),A), rootEnvironmentContext()], IMPLIES(A,IMPLIES(B,C)));
newSection("7", "Push");
exerciseFromData("7.1", [formulaContext(A), formulaContext(B)], IMPLIES(A, IMPLIES(B,A)));
exerciseFromData("7.2", [A, environmentContext([B,C])], assuming(assuming(A,C),B));
newSection("8", "Modus ponens");
exerciseFromData("8.1(a)", [A, assuming(B,A)], B);
exerciseFromData("8.1(b)", [IMPLIES(A,B)], assuming(B,A),5);
exerciseFromData("8.2", [IMPLIES(A,B), IMPLIES(B,C)], IMPLIES(A,C));
exerciseFromData("8.3", [formulaContext(A), formulaContext(B)], IMPLIES(AND(A,B),AND(B,A)));
exerciseFromData("8.4(a)", [IMPLIES(A,IMPLIES(B,C))], IMPLIES(AND(A,B),C));
exerciseFromData("8.4(b)", [IMPLIES(AND(A,B),C)], IMPLIES(A,IMPLIES(B,C)));
exerciseFromData("8.4(c)", [IMPLIES(A,IMPLIES(B,C))], IMPLIES(B,IMPLIES(A,C)));
exerciseFromData("8.5(a)", [IMPLIES(A,B)], IMPLIES(A, AND(A,B)));
exerciseFromData("8.5(b)", [IMPLIES(A,B)], IMPLIES(A, AND(B,A)));
exerciseFromData("8.6(a)", [AND(A,B), IMPLIES(A,C)], AND(C,B));
exerciseFromData("8.6(b)", [AND(A,B), IMPLIES(B,C)], AND(A,C));
newSection("9", "Case analysis");
exerciseFromData("9.1(a)", [OR(A,B)], OR(B,A));
exerciseFromData("9.1(b)", [OR(A,A)], A);
exerciseFromData("9.2(a)", [OR(OR(A,B),C)], OR(A,OR(B,C)));
exerciseFromData("9.2(b)", [OR(A,OR(B,C))], OR(OR(A,B),C));
exerciseFromData("9.3(a)", [OR(A, AND(B,C))], AND(OR(A,B), OR(A,C)));
exerciseFromData("9.3(b)", [AND(A, OR(B,C))], OR(AND(A,B), AND(A,C)));
exerciseFromData("9.3(c)", [OR(AND(A,B), AND(A,C))], AND(A, OR(B,C)));
exerciseFromData("9.3(d)", [AND(OR(A,B), OR(A,C))], OR(A, AND(B,C)));
exerciseFromData("9.4(a)", [OR(A,B), IMPLIES(A,C)], OR(C,B));
exerciseFromData("9.4(b)", [OR(A,B), IMPLIES(B,C)], OR(A,C));
exerciseFromData("9.4(c)", [OR(A,B), IMPLIES(A,C), IMPLIES(B,D)], OR(C,D));
exerciseFromData("9.5(a)", [formulaContext(C), IMPLIES(A,B)], IMPLIES(AND(A,C), AND(B,C)));
exerciseFromData("9.5(b)", [formulaContext(C), IMPLIES(A,B)], IMPLIES(OR(A,C), OR(B,C)));
exerciseFromData("9.5(c)", [formulaContext(C), IMPLIES(A,B)], IMPLIES(AND(C,A), AND(C,B)));
exerciseFromData("9.5(d)", [formulaContext(C), IMPLIES(A,B)], IMPLIES(OR(C,A), OR(C,B)));
newSection("10", "The biconditional");
exerciseFromData("10.1(a)", [A, IFF(A,B)], B);
exerciseFromData("10.1(b)", [AND(A,B), IFF(A,C)], AND(C,B));
exerciseFromData("10.1(c)", [AND(A,B), IFF(B,C)], AND(A,C));
exerciseFromData("10.1(d)", [OR(A,B), IFF(A,C)], OR(C,B));
exerciseFromData("10.1(e)", [OR(A,B), IFF(B,C)], OR(A,C));
exerciseFromData("10.1(f)", [IMPLIES(A,B), IFF(A,C)], IMPLIES(C,B));
exerciseFromData("10.1(g)", [IMPLIES(A,B), IFF(B,C)], IMPLIES(A,C));
exerciseFromData("10.2(a)", [IFF(A,B)], IFF(B,A));
exerciseFromData("10.2(b)", [IFF(A,B), IFF(B,C)], IFF(A,C));
exerciseFromData("10.2(c)", [formulaContext(A)], IFF(A,A));
exerciseFromData("10.3", [assuming(A,B), assuming(B,A)], IFF(A,B));
exerciseFromData("10.4", [formulaContext(A)], IFF(A, OR(A,A)));
exerciseFromData("10.5", [formulaContext(A), formulaContext(B), formulaContext(C)], IFF(AND(AND(A,B),C),AND(A,AND(B,C))));
newSection("11", "Disjunctive elimination");
exerciseFromData("11.1", [AND(A,NOT(A)), formulaContext(B)], B);
exerciseFromData("11.2", [AND(NOT(A),A), formulaContext(B)], B);
newSection("12", "Law of excluded middle");
exerciseFromData("12.1(a)", [assuming(AND(B,NOT(B)),A)], NOT(A));
exerciseFromData("12.1(b)", [assuming(B,A), assuming(NOT(B),A)], NOT(A));
exerciseFromData("12.1(c)", [assuming(B,A), assuming(B,NOT(A))], B);
exerciseFromData("12.1(d)", [formulaContext(A)], OR(NOT(A),A));
exerciseFromData("12.2(a)", [NOT(NOT(A))], A);
exerciseFromData("12.2(b)", [A], NOT(NOT(A)));
exerciseFromData("12.2(c)", [formulaContext(A)], IFF(A,NOT(NOT(A))));
exerciseFromData("12.3(a)", [assuming(AND(B,NOT(B)),NOT(A))], A);
exerciseFromData("12.3(b)", [assuming(AND(NOT(B),B),NOT(A))], A);
exerciseFromData("12.4(a)", [IMPLIES(A,B)], OR( NOT(A), B));
exerciseFromData("12.4(b)", [OR( NOT(A), B)], IMPLIES(A,B));
exerciseFromData("12.4(c)", [formulaContext(A), formulaContext(B)], IFF(IMPLIES(A,B), OR( NOT(A), B)));
exerciseFromData("12.5(a)", [NOT(OR(A,B))], AND(NOT(A), NOT(B)));
exerciseFromData("12.5(b)", [OR(NOT(A), NOT(B))], NOT(AND(A,B)));
exerciseFromData("12.5(c)", [NOT(AND(A,B))], OR(NOT(A), NOT(B)));
exerciseFromData("12.5(d)", [AND(NOT(A), NOT(B))], NOT(OR(A,B)));
exerciseFromData("12.6(a)", [IMPLIES(A,B)], IMPLIES(NOT(B),NOT(A)));
exerciseFromData("12.6(b)", [IMPLIES(A,B), NOT(B)], NOT(A));
exerciseFromData("12.6(c)", [NOT(A), IFF(A,B)], NOT(B));
exerciseFromData("12.7", [IMPLIES(IMPLIES(A,B),A)], A);
exerciseFromData("12.8", [OR(A,B), OR(NOT(A),C)], OR(C,B));
newSection("13", "True and false");
exerciseFromData("13.1(a)", [formulaContext(A)], IFF(A,AND(TRUE(),A)),7);
exerciseFromData("13.1(b)", [formulaContext(A)], IFF(A,OR(FALSE(),A)));
exerciseFromData("13.2(a)", [formulaContext(A)], NOT(AND(FALSE(),A)));
exerciseFromData("13.2(b)", [formulaContext(A)], OR(TRUE(),A));
exerciseFromData("13.3(a)", [formulaContext(A)], IMPLIES(FALSE(),A));
exerciseFromData("13.3(b)", [formulaContext(A)], IMPLIES(A,TRUE()));
exerciseFromData("13.3(c)", [formulaContext(A)], IFF(A, IMPLIES(TRUE(),A)));
exerciseFromData("13.3(d)", [formulaContext(A)], IFF(NOT(A), IMPLIES(A,FALSE())));
newSection("14", "Free variables");
exerciseFromData("14.1", [assuming(Px,x)], assuming(IMPLIES(Qx,AND(Px,Qx)),x));
newSection("15", "Push (for free variables)");
exerciseFromData("15.1", [assuming(Px,x), assuming(assuming(Qxy,y),x)], assuming(assuming(AND(Px,Qxy),y),x));
exerciseFromData("15.2(a)", [A, environmentContext([x,y])], assuming(assuming(A,y),x));
exerciseFromData("15.2(b)", [A, environmentContext([B,x])], assuming(assuming(A,x),B));
exerciseFromData("15.2(c)", [A, environmentContext([x,B])], assuming(assuming(A,B),x));
newSection("16", "Free variable introduction");
new Law("free", "FREE VARIABLE INTRODUCTION", [toTerm(x)], x);
exerciseFromData("16.1", [formulaContext(Qxy)], assuming(assuming(OR(Qxy, NOT(Qxy)),y),x));
newSection("17", "Universal quantification");
exerciseFromData("17.1", [formulaContext(Px)], forAll(IMPLIES(PX,PX),X));
exerciseFromData("17.2", [formulaContext(QXY)], IMPLIES(forAll(forAll(QXY,Y),X),forAll(forAll(QXY,Y),X)));
newSection("18", "Universal specification");
new Exercise("18.1", universalRenamingBoundVar);
exerciseFromData("18.2(a)", [A, toTerm(X)], forAll(A,X));
new Exercise("18.2(b)", universalSpecification2);
exerciseFromData("18.3(a)", [forAll(IMPLIES(PX,QX),X), Pa], Qa);
exerciseFromData("18.3(b)", [forAll(IMPLIES(PX,QX),X), forAll(IMPLIES(RX,PX),X)], forAll(IMPLIES(RX,QX),X));
exerciseFromData("18.4", [forAll(forAll(QXY,Y),X)], forAll(forAll(QXY,X),Y));
exerciseFromData("18.5", [formulaContext(PX), formulaContext(QX)], IFF( forAll( AND(PX,QX), X ), AND(forAll(PX,X), forAll(QX,X))));
exerciseFromData("18.6", [formulaContext(A), formulaContext(PX)], IFF( IMPLIES(A, forAll( PX, X )), forAll(IMPLIES(A,PX),X)));
newSection("19", "Existential quantification");
exerciseFromData("19.1", [thereExists(PX,X), forAll(QX,X)], assuming(AND(Px,Qx), settingAssumption(Px,x)));
exerciseFromData("19.2(a)", [A, environmentContext([B, settingAssumption(C,x)])], assuming(assuming(A,settingAssumption(C,x)),B));
exerciseFromData("19.2(b)", [A, environmentContext([settingAssumption(C,x), B])], assuming(assuming(A,B),settingAssumption(C,x)));
exerciseFromData("19.2(c)", [A, environmentContext([settingAssumption(C,x), y])], assuming(assuming(A,y),settingAssumption(C,x)));
exerciseFromData("19.2(d)", [A, environmentContext([y,settingAssumption(C,x)])], assuming(assuming(A,settingAssumption(C,x)),y));
exerciseFromData("19.2(e)", [A, environmentContext([settingAssumption(B,y),settingAssumption(C,x)])], assuming(assuming(A,settingAssumption(C,x)),settingAssumption(B,y)));
newSection("20", "Pull");
exerciseFromData("20.1", [thereExists(A,X)], A);
exerciseFromData("20.2", [assuming(assuming(A, settingAssumption(B,x)),settingAssumption(C,y)),rootEnvironmentContext()], A);
newSection("21", "Existence");
exerciseFromData("21.1", [assuming(A, x), rootEnvironmentContext()], A);
newSection("22", "Existential introduction");
exerciseFromData("22.1", [Qaa], thereExists(AND(QaX,QXa),X));
exerciseFromData("22.2", [forAll(PX,X)], thereExists(PX,X));
exerciseFromData("22.3(a)", [formulaContext(PX), formulaContext(Px), X], IFF( NOT(thereExists(PX, X)), forAll(NOT(PX),X)));
exerciseFromData("22.3(b)", [formulaContext(PX), formulaContext(Px), X], IFF( NOT(forAll(PX, X)), thereExists(NOT(PX),X)));
exerciseFromData("22.4(a)", [NOT(thereExists(AND(PX,QX),X)), forAll(IMPLIES(RX,PX),X), formulaContext(Px), formulaContext(Qx), formulaContext(Rx)], NOT(thereExists(AND(RX,QX),X)));
exerciseFromData("22.4(b)", [forAll(IMPLIES(PX,QX),X), thereExists(AND(RX,PX),X)], thereExists(AND(RX,QX),X));
exerciseFromData("22.4(c)", [NOT(thereExists(AND(PX,QX),X)), thereExists(AND(RX,PX),X), formulaContext(Px), formulaContext(Qx), formulaContext(Rx)], thereExists(AND(RX,NOT(QX)),X));
exerciseFromData("22.4(d)", [forAll(IMPLIES(PX,QX), X), thereExists(AND(RX,NOT(QX)),X)], thereExists(AND(RX,NOT(PX)),X));
exerciseFromData("22.4(e)", [thereExists(AND(PX, NOT(QX)), X), forAll(IMPLIES(PX,RX), X), formulaContext(Px), formulaContext(Qx), formulaContext(Rx)], thereExists(AND(RX,NOT(QX)),X));
exerciseFromData("22.5(a)", [forAll(IMPLIES(PX,QX), X), forAll(IMPLIES(QX,RX),X), thereExists(PX, X)], thereExists(AND(PX,RX),X));
exerciseFromData("22.5(b)", [NOT(thereExists(AND(PX,QX),X)), forAll(IMPLIES(RX,PX),X), thereExists(RX, X), formulaContext(Px), formulaContext(Qx), formulaContext(Rx)], thereExists(AND(RX,NOT(QX)),X));
exerciseFromData("22.5(c)", [forAll(IMPLIES(PX,QX),X), NOT(thereExists(AND(RX,QX),X)), thereExists(RX,X), formulaContext(Px), formulaContext(Qx), formulaContext(Rx)], thereExists(AND(RX,NOT(PX)),X));
exerciseFromData("22.5(d)", [NOT(thereExists(AND(PX,QX),X)), forAll(IMPLIES(PX,RX),X), thereExists(PX,X), formulaContext(Px), formulaContext(Qx), formulaContext(Rx)], thereExists(AND(RX, NOT(QX)),X));
exerciseFromData("22.5(e)", [forAll(IMPLIES(PX,QX),X), forAll(IMPLIES(PX,RX),X), thereExists(PX,X)], thereExists(AND(RX, QX),X));
exerciseFromData("22.6(a)", [thereExists(thereExists(QXY,X),Y)], thereExists(thereExists(QXY,Y),X));
exerciseFromData("22.6(b)", [thereExists(forAll(QXY,X),Y)], forAll(thereExists(QXY,Y),X));
exerciseFromData("22.7", [formulaContext(Px), formulaContext(Qy)], IFF( AND(thereExists(PX,X), thereExists(QY,Y)), thereExists(thereExists(AND(PX,QY),Y),X)));
exerciseFromData("22.8", [forAll(IMPLIES(PX,NOT(QX)),X), forAll(IMPLIES(NOT(QX),RX),X), NOT(thereExists(AND(RX,SX),X)), formulaContext(Px), formulaContext(Qx), formulaContext(Rx), formulaContext(Sx)], forAll(IMPLIES(PX, NOT(SX)),X));
newSection("23", "Predicates and operators");
exerciseFromData("23.1(a)", [], forAll(forAll(IMPLIES(QXY,QXY),Y),X));
exerciseFromData("23.1(b)", [], forAll(forAll(IMPLIES(gtXY,gtXY),Y),X));
exerciseFromData("23.1(c)", [], forAll(forAll(IMPLIES(PXplusY,PXplusY),Y),X));
exerciseFromData("23.2", [thereExists(forAll(IFF(YinX,NOT(YinY)),Y),X)], NOT(TRUE()));
exerciseFromData("23.3", [forAll(NOT(XgteX1),X)], NOT(thereExists(forAll(XgteY,Y),X)));
newSection("24", "Equality");
exerciseFromData("24.1(a)", [equals(alpha,beta)], equals(beta,alpha));
exerciseFromData("24.1(b)", [equals(alpha,beta), equals(beta,gamma)], equals(alpha,gamma));
exerciseFromData("24.2", [equals(alpha,beta)], equals(fa,fb));
exerciseFromData("24.3", [forAll(equals(multiply(alpha,X),X),X), forAll(equals(multiply(X,beta),X),X)], equals(alpha,beta));
exerciseFromData("24.4", [forAll(equals(multiply(one,X),X),X), forAll(forAll(forAll(equals(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)), Z), Y), X), forAll(thereExists(equals(multiply(Y,X),one),Y),X), equals(multiply(alpha,beta),multiply(alpha,gamma))], equals(beta,gamma));
exerciseFromData("24.5", [forAll(equals(multiply(one,X),X),X), forAll(forAll(forAll(equals(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)), Z), Y), X), thereExists(equals(multiply(X,alpha),one),X), thereExists(equals(multiply(X,beta),one),X)], thereExists(equals(multiply(X,multiply(alpha,beta)),one),X));
exerciseFromData("24.6", [forAll(equals(multiply(one,X),X),X), forAll(equals(multiply(X,one),X),X), forAll(forAll(forAll(equals(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)), Z), Y), X), forAll(equals(multiply(fX,X),one),X)], forAll(equals(ffX,X),X));
exerciseFromData("24.7", [forAll(forAll(forAll(equals(power(power(X,Y),Z), power(X,multiply(Y,Z))),Z),Y),X), forAll(equals(multiply(sqrtX, sqrtX),X),X), forAll(equals(power(sqrtX,two),X),X), predicateSentence(R,[two]), NOT(predicateSentence(R,[sqrt2]))], thereExists(thereExists(AND(AND(NOT(RX),NOT(RY)), predicateSentence(R,[power(X,Y)])), Y), X));
// load notes, proofs, best length, and unlockedBy for exercises from HTML
exerciseList.forEach( function( exercise ) {
var div = getElement("EXERCISE-"+exercise.shortName);
if (div == null) return;
var unlockedBy;
if (unlockedBy = div.getAttribute("data-unlocked-by")) {
var unlocker = exercisesByShortName[unlockedBy];
exercise.unlockedBy(unlocker);
} else {
// Otherwise, this is the first exercise.
activateExerciseButton(exercise);
}
var unlocks;
if (unlocks = div.getAttribute("data-unlocks")) {
var split = unlocks.split(" ");
split.forEach( function( str ) {
exercise.unlocks(lawsByShortName[str]);
} );
}
var revealTarget;
if (revealTarget = div.getAttribute("data-reveals")) {
// For example, sets exercise.revealBoundButton to true.
exercise["reveal" + revealTarget] = true;
}
if (div.getElementsByClassName("name").length > 0) {
var str = div.getElementsByClassName("name")[0].innerHTML;
if (str != "")
{
exercise.law.name = str;
// need to assign name to the clone of law as well
if (exercise.law.clone != "") exercise.law.clone.name = exercise.law.name;
}
}
if (div.getElementsByClassName("notes").length > 0)
exercise.notes = div.getElementsByClassName("notes")[0].innerHTML;
if (div.getElementsByClassName("proof").length > 0) {
var proof = div.getElementsByClassName("proof")[0];
exercise.proof= proof.innerHTML;
exercise.bestLength = proof.getElementsByTagName("LI").length;
}
colorExerciseButton(exercise.button, false);
});
// this command has to be executed after all laws and exercises defined and all GUI elements are in place
checkForUnlocks();