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Commit 2630d3b1 authored by Björn Brandenburg's avatar Björn Brandenburg
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do not rely on vlib 'des' tactic

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...@@ -10,7 +10,7 @@ Section BigCatLemmas. ...@@ -10,7 +10,7 @@ Section BigCatLemmas.
x \in (f j) -> x \in (f j) ->
x \in \cat_(m <= i < n) (f i). x \in \cat_(m <= i < n) (f i).
Proof. Proof.
intros T x m n j f LE IN; move: LE => /andP LE; des. intros T x m n j f LE IN; move: LE => /andP [LE LE0].
rewrite -> big_cat_nat with (n := j); simpl; [| by ins | by apply ltnW]. rewrite -> big_cat_nat with (n := j); simpl; [| by ins | by apply ltnW].
rewrite mem_cat; apply/orP; right. rewrite mem_cat; apply/orP; right.
destruct n; first by rewrite ltn0 in LE0. destruct n; first by rewrite ltn0 in LE0.
...@@ -30,7 +30,7 @@ Section BigCatLemmas. ...@@ -30,7 +30,7 @@ Section BigCatLemmas.
rewrite big_nat_recr // /= mem_cat in IN. rewrite big_nat_recr // /= mem_cat in IN.
move: IN => /orP [HEAD | TAIL]. move: IN => /orP [HEAD | TAIL].
{ {
apply IHn in HEAD; destruct HEAD; exists x0; des. apply IHn in HEAD; destruct HEAD; exists x0. move: H => [H /andP [H0 H1]].
split; first by done. split; first by done.
by apply/andP; split; [by done | by apply ltnW]. by apply/andP; split; [by done | by apply ltnW].
} }
...@@ -157,4 +157,4 @@ Section BigCatLemmas. ...@@ -157,4 +157,4 @@ Section BigCatLemmas.
by apply leq_sum; ins; apply SIZE. by apply leq_sum; ins; apply SIZE.
Qed. Qed.
End BigCatLemmas. End BigCatLemmas.
\ No newline at end of file
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