26 lines
528 B
Coq
26 lines
528 B
Coq
(*
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https://coq.zulipchat.com/#narrow/stream/237977-Coq-users/topic/Project.20nth.20element.20of.20n-tuple
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Soln by guillaume melquiond: https://www.lri.fr/~melquion/index.html.en
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*)
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Require Import List.
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Definition nth_tup {l : list Type}:
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forall (x:fold_right prod unit l) (n:nat), nth n l unit.
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Proof.
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induction l as [|A l IH].
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- intros _ [|] ; exact tt.
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- intros [a b] [|n].
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exact a.
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now apply IH.
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Restart.
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induction l.
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- intros _ [|].
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+ exact tt.
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+ exact tt.
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- intros H n.
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apply (IHl H).
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Defined.
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