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[Francisco Ferreira <fco AT 42nd.ca>]

Hello everybody,
I defined the following data type
Inductive Acc (A : Set) (R : A -> A -> Prop) (t : A): Prop :=
inj : (forall t': A, R t t' -> Acc A R t') -> Acc A R t.
and I am trying to prove a lemma by induction on it. For example, it has
the following shape.
Lemma test: forall m n, Acc nat gt (m + n) -> Acc nat gt m.
Trying to do induction on (Acc nat gt (m + n)) leads us to an hypothesis
H0 : forall t' : nat, t > t' -> Acc nat gt m
where t has no relation with m and n.
Trying to use the remember tactics
intros.
remember (m + n) as t.
induction H.
leads us to an induction hypothesis
H0 : forall t' : nat, t > t' -> t' = m + n -> Acc nat gt m
but the clause t' = m + n is unsatisfiable for any t' < t.
How I can use induction on Acc in such a way that the induction
hypothesis preserves the information and is still usable?
Thanks,
Francisco

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