diff --git a/Cslib/Computability/Distributed/FLP/ZeroConsensus.lean b/Cslib/Computability/Distributed/FLP/ZeroConsensus.lean index 96d885a87..0feba1945 100644 --- a/Cslib/Computability/Distributed/FLP/ZeroConsensus.lean +++ b/Cslib/Computability/Distributed/FLP/ZeroConsensus.lean @@ -33,7 +33,7 @@ namespace Cslib.FLP.ZeroFaultAlg open Set Sum Option Multiset ωSequence /-- The payload of a message is of type `Bool ⊕ Bool`, where `inl b` denotes an input value `b` -ane `inr b` denotes a value `b` sent by process 0 to all processes (including itself). -/ +and `inr b` denotes a value `b` sent by process 0 to all processes (including itself). -/ abbrev M := Bool /-- The local state of a process is trivial. -/ diff --git a/Cslib/Computability/Languages/MyhillNerode.lean b/Cslib/Computability/Languages/MyhillNerode.lean index f22fe8646..e42d3d325 100644 --- a/Cslib/Computability/Languages/MyhillNerode.lean +++ b/Cslib/Computability/Languages/MyhillNerode.lean @@ -23,7 +23,7 @@ The Myhill-Nerode theorem has three parts [WikipediaMyhillNerode2026]: (3) The minimal DFA is unique up to unique isomorphism. That is, for any minimal DFA accepting `l`, there exists exactly an isomorphism from it to the - canonical DFA whose states are the equivalence classses of `c_l`, whose + canonical DFA whose states are the equivalence classes of `c_l`, whose state transitions are of the form `⟦ x ⟧ → ⟦ x ++ [a] ⟧` (where `a : α` and `x : List α`), whose initial state is `⟦ [] ⟧`, and whose accepting states are `{ ⟦ x ⟧ | x ∈ l }`. diff --git a/Cslib/Foundations/Relation/Defs.lean b/Cslib/Foundations/Relation/Defs.lean index f649ed5dd..888e64c46 100644 --- a/Cslib/Foundations/Relation/Defs.lean +++ b/Cslib/Foundations/Relation/Defs.lean @@ -85,7 +85,7 @@ abbrev Normalizable (r : α → α → Prop) (x : α) : Prop := abbrev Normalizing (r : α → α → Prop) : Prop := ∀ x, Normalizable r x -/-- An element `x` is `SN` (for strongly-normalising) for a relation `r` if it is accesible under +/-- An element `x` is `SN` (for strongly-normalising) for a relation `r` if it is accessible under the inverse of `r`. -/ abbrev SN (r : α → α → Prop) := Acc (fun a b => r b a) diff --git a/Cslib/Foundations/Semantics/LTS/Basic.lean b/Cslib/Foundations/Semantics/LTS/Basic.lean index b1f864f89..ae62ed778 100644 --- a/Cslib/Foundations/Semantics/LTS/Basic.lean +++ b/Cslib/Foundations/Semantics/LTS/Basic.lean @@ -148,7 +148,7 @@ theorem MTr.single_invert (s1 : State) (μ : Label) (s2 : State) : cases hmtr exact htr -/-- A 1-sized multistep transition is exactly a single transision with the given label. -/ +/-- A 1-sized multistep transition is exactly a single transition with the given label. -/ @[simp] theorem MTr.singleton_iff (s1 : State) (μ : Label) (s2 : State) : lts.MTr s1 [μ] s2 ↔ lts.Tr s1 μ s2 := ⟨MTr.single_invert lts s1 μ s2, MTr.single lts⟩ diff --git a/Cslib/Foundations/Semantics/LTS/TraceEq.lean b/Cslib/Foundations/Semantics/LTS/TraceEq.lean index 45782b67a..700ddf0c3 100644 --- a/Cslib/Foundations/Semantics/LTS/TraceEq.lean +++ b/Cslib/Foundations/Semantics/LTS/TraceEq.lean @@ -136,19 +136,19 @@ theorem HomTraceEq.eqv : Equivalence (· ~tr[lts] ·) where instance : Trans (TraceEq lts₁ lts₂) (TraceEq lts₂ lts₃) (TraceEq lts₁ lts₃) where trans := TraceEq.trans -/-- For trace-equivalent states, any multistep transition of one can be mimiced by the other. -/ +/-- For trace-equivalent states, any multistep transition of one can be mimicked by the other. -/ theorem TraceEq.exists_mTr_of_mTr {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label} (h : s₁ ~tr[lts₁,lts₂] s₂) (htr : lts₁.MTr s₁ μs s₁') : ∃ s₂', lts₂.MTr s₂ μs s₂' := by rw [←mem_traces_iff, ←h] exact ⟨s₁', htr⟩ -/-- For trace-equivalent states, any single-step transition of one can be mimiced by the other. -/ +/-- For trace-equivalent states, any single-step transition of one can be mimicked by the other. -/ theorem TraceEq.exists_tr_of_tr {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label} (h : s₁ ~tr[lts₁,lts₂] s₂) (htr : lts₁.Tr s₁ μ s₁') : ∃ s₂', lts₂.Tr s₂ μ s₂' := by rw [←mem_traces_singleton_iff, ←h, mem_traces_singleton_iff] exact ⟨s₁', htr⟩ -/-- For deterministic lts's, trace equivalence is preseved by respective transitions with the same +/-- For deterministic lts's, trace equivalence is preserved by respective transitions with the same label. -/ theorem TraceEq.traceEq_of_tr_of_tr {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label} [hdet₁ : lts₁.Deterministic] [hdet₂ : lts₂.Deterministic] (h : s₁ ~tr[lts₁,lts₂] s₂) diff --git a/Cslib/Logics/Modal/Basic.lean b/Cslib/Logics/Modal/Basic.lean index 017c60ec9..048c650e8 100644 --- a/Cslib/Logics/Modal/Basic.lean +++ b/Cslib/Logics/Modal/Basic.lean @@ -145,7 +145,7 @@ This result proves that the definition is correct. -/ theorem Satisfies.box_iff_forall {m : Model World Atom} : ⇓Modal[m,w ⊨ □φ] ↔ ∀ w', m.r w w' → ⇓Modal[m,w' ⊨ φ] := by grind [Proposition.box] -/-- The theory of a world in a model is the set of all propositions that it satifies. -/ +/-- The theory of a world in a model is the set of all propositions that it satisfies. -/ abbrev theory (m : Model World Atom) (w : World) : Set (Proposition Atom) := {φ | ⇓Modal[m,w ⊨ φ]}