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@mzp mzp/Zakky.v
Created Aug 2, 2014

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Inductive Term : Set :=
| T
| F
| TIf (_ : Term) (_ : Term) (_ : Term).
Inductive Step : Term -> Term -> Prop :=
| EIfTrue : forall (t1 t2 : Term), Step (TIf T t1 t2) t1
| EIfFalse : forall (t1 t2 : Term), Step (TIf F t1 t2) t2
| EIf : forall (t1 t1' t2 t3 : Term), Step t1 t1' -> Step (TIf t1 t2 t3) (TIf t1' t2 t3).
Lemma dec: forall (t t' t'' : Term),
Step t t' -> Step t t'' -> t' = t''.
Check Step_ind.
intros t t' t'' Q.
generalize t''.
apply Step_ind with (t:=t) (t0:=t'); intros; auto.
inversion H; auto.
inversion H4.
inversion H; auto.
inversion H4.
destruct t1.
inversion H.
inversion H.
inversion H1.
apply H0 in H6.
rewrite H6.
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