# gruninger/colore

new theories in ringoid and ordered_ringoid

michael.gruninger committed Jan 29, 2015
1 parent a6985b9 commit f67e2acc4b682640b66fe8c54440bd6b4ebf7b49
 @@ -0,0 +1,30 @@ (cl-text http://colore.oor.net/ordered_ringoid/discrete_ordered_ring.clif (cl-imports http://colore.oor.net/ringoids/ring.clif) (cl-imports http://colore.oor.net/orderings/linear_ordering.clif) (cl-imports http://colore.oor.net/orderings/definitions/ordering_defs.clif) (forall (x y z) (if (lt x y) (lt (sum x z) (sum y z)))) (forall (x y z) (if (and (lt zero x) (lt x y)) (lt (prod x z) (prod y z)))) (forall (x y) (if (lt x y) (exists (z) (= y (sum x z))))) (lt zero one) (forall (x) (if (lt zero x) (leq one x))) )
 @@ -0,0 +1,30 @@ (cl-text http://colore.oor.net/ordered_ringoid/discrete_ordered_semiring.clif (cl-imports http://colore.oor.net/ringoids/semiring.clif) (cl-imports http://colore.oor.net/orderings/linear_ordering.clif) (cl-imports http://colore.oor.net/orderings/definitions/ordering_defs.clif) (forall (x y z) (if (lt x y) (lt (sum x z) (sum y z)))) (forall (x y z) (if (and (lt zero x) (lt x y)) (lt (prod x z) (prod y z)))) (forall (x y) (if (lt x y) (exists (z) (= y (sum x z))))) (lt zero one) (forall (x) (if (lt zero x) (leq one x))) )
 @@ -1,7 +1,7 @@ (cl-text http://colore.oor.net/ordered_ringoid/euclidean_field (cl-text http://colore.oor.net/ordered_ringoid/euclidean_field.clif (cl-imports http://colore.oor.net/ordered_ringoid/ordered_field) (cl-imports http://colore.oor.net/ordered_ringoid/ordered_field.clif) (forall (x) (if (leq zero x)
 @@ -1,9 +1,9 @@ (cl-text http://colore.oor.net/ordered_ringoid/ordered_field (cl-text http://colore.oor.net/ordered_ringoid/ordered_field.clif (cl-imports http://colore.oor.net/ringoids/field) (cl-imports http://colore.oor.net/ringoids/field.clif) (cl-imports http://colore.oor.net/orderings/linear_ordering) (cl-imports http://colore.oor.net/orderings/linear_ordering.clif) (forall (x y z) (if (leq x y)
 @@ -0,0 +1,9 @@ (cl-text http://colore.oor.net/ringoids/commutative_semiring.clif (cl-imports http://colore.oor.net/ringoids/semiring.clif) (forall (x y) (= (prod x y) (prod y x))) )
 @@ -0,0 +1,9 @@ (cl-text http://colore.oor.net/ringoids/idempotent_semiring.clif (cl-imports http://colore.oor.net/ringoids/semiring.clif) (forall (x) (= x (sum x x))) )
 @@ -0,0 +1,31 @@ (cl-text http://colore.oor.net/ringoids/semiring.clif (forall (x y z) (= (sum (sum x y) z) (sum x (sum y z)))) (forall (x) (and (= x (sum zero x)) (= x (sum x zero)))) (forall (x y) (= (sum x y) (sum y x))) (forall (x y z) (= (prod (prod x y) z) (prod x (prod y z)))) (forall (x) (and (= x (prod one x)) (= x (prod x one)))) (forall (x) (and (= zero (prod zero x)) (= zero (prod x zero)))) (forall (x y z) (= (prod x (sum y z)) (sum (prod x y) (prod x z)))) (forall (x y z) (= (prod (sum x y) z) (sum (prod x z) (prod y z)))) )