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Farcry3trainer0101

Jun 26, 2013

Category:Programming languages
Category:Far Cry
Category:Computer-related introductions in 2000
Category:Video game development softwareQ:

How to convert a set of the form $\{P | Q\}$ to the type $\{P\} \Rightarrow \{Q\}$ in Coq?

I’m trying to work out some tricky proofs with dependent types in Coq.
In order to do this, I have to prove things like the following:
lemma nat_prod_assoc_correct {a b c} (h1 h2 : a * b) (h3 : a + c = c + a) :
h1 * (h2 * h3) = h1 * h2 * h3.
Proof.
intro h.
simpl h1.
simpl h2.
intro ht.
induction ht using simpa_induction with h1, h3; intros;
simpl ht.
auto.
Qed.

Of course, this doesn’t work, since the proof branch with ht has more than one hypothesis.
Furthermore, I would want to write proofs like
lemma nat_prod_assoc_correct {a b c} (h1 h2 : a * b) (h3 : a + c = c + a) :
h1 * (h2 * h3) = h1 * h2 * h3.
Proof.
intro h.
simpl h1.
simpl h2.
induction h3 using induction with h1.
simpl h1.
simpl h2.
intro ht.
induction ht using simpa_induction with h1.
auto.
Qed.

where I would want to write something like simpa_induction with h1 on a generic family of hypotheses that always hold in that proof branch.
The question: How would I go about doing this? I realise that what I’m asking to do seems like a very simple thing, but the Coq manual is mostly silent on this issue.

A:

Finally I came up with the following solution.
Require Import MultCat.

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