Thms choice 1 Sections AutomataTheory Doc

NOTE: This operator coercing a to a Prop is normally invisible since it is pretty obvious when it is needed.

assert Def b == if b True else False fi

Thm* b:. b Prop

equiv_rel Def EquivRel x,y:T. E(x;y) == Refl(T;x,y.E(x;y)) & Sym x,y:T. E(x;y) & Trans x,y:T. E(x;y)

Thm* T:Type, E:(TTProp). (EquivRel x,y:T. E(x,y)) Prop

iff Def P Q == (P Q) & (P Q)

Thm* A,B:Prop. (A B) Prop

trans Def Trans x,y:T. E(x;y) == a,b,c:T. E(a;b) E(b;c) E(a;c)

Thm* T:Type, E:(TTProp). Trans x,y:T. E(x,y) Prop

sym Def Sym x,y:T. E(x;y) == a,b:T. E(a;b) E(b;a)

Thm* T:Type, E:(TTProp). Sym x,y:T. E(x,y) Prop

refl Def Refl(T;x,y.E(x;y)) == a:T. E(a;a)

Thm* T:Type, E:(TTProp). Refl(T;x,y.E(x,y)) Prop

rev_implies Def P Q == Q P

Thm* A,B:Prop. (A B) Prop

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!abstractionimpliesallpropmemberuniversefunction
andifthenelsetruefalseboolassert