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Adapt to math-comp/math-comp#1125 #1271

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Adapt to math-comp/math-comp#1125 #1271

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6 changes: 3 additions & 3 deletions theories/derive.v
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Original file line number Diff line number Diff line change
Expand Up @@ -509,7 +509,7 @@ apply/ler_gtP => _ /posnumP[e]; rewrite ler_pdivrMr //.
have /oid /nbhs_ballP [_ /posnumP[d] dfe] := !! gt0 e.
set k := ((d%:num / 2) / (PosNum xn0)%:num)^-1.
rewrite -{1}(@scalerKV _ _ k _ x) /k // linearZZ normrZ.
rewrite -ler_pdivlMl; last by rewrite gtr0_norm.
rewrite -ler_pdivlMl; last by rewrite gtr0_norm invr_gt0.
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Well, the actual source of the issue I have is that the goal after rewrite gtr0_norm is now:

0 < idfun (d%:num / 2 / (PosNum xn0)%:num)^-1

where idfun is actually a homomorphism application:

GRing.RMorphism.sort (reverse_coercion (GRing.ssrfun_idfun__canonical__GRing_RMorphism ...) idfun)

simpl unfolds (PosNum xn0)%:num and thus is too aggressive here. Declaring a signed instance for homomorphisms would require the structures of order-preserving additive functions and ring homomorphisms, which we don't have in Mathcomp yet.

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I also expected the canonical structure inference to unfold this homomorphism application automatically, but is it because of the presence of a default instance that it does not happen?

rewrite mulrCA (@le_trans _ _ (e%:num * `|k^-1 *: x|)) //; last first.
by rewrite ler_pM // normrZ normfV.
apply: dfe; rewrite -ball_normE /= sub0r normrN normrZ.
Expand Down Expand Up @@ -773,9 +773,9 @@ rewrite -[`|u|]/((PosNum un0)%:num) -[`|v|]/((PosNum vn0)%:num).
set ku := 2 / e%:num * (PosNum un0)%:num.
set kv := 2 / e%:num * (PosNum vn0)%:num.
rewrite -[X in f X](@scalerKV _ _ ku) /ku // linearZl_LR normrZ.
rewrite gtr0_norm // -ler_pdivlMl //.
rewrite gtr0_norm ?mulr_gt0 //= -ler_pdivlMl ?mulr_gt0 //=.
rewrite -[X in f _ X](@scalerKV _ _ kv) /kv // linearZr_LR normrZ.
rewrite gtr0_norm // -ler_pdivlMl //.
rewrite gtr0_norm ?mulr_gt0 // -ler_pdivlMl ?mulr_gt0 //=.
suff /he : ball 0 e%:num (ku^-1 *: u, kv^-1 *: v).
rewrite -ball_normE /= distrC subr0 => /ltW /le_trans; apply.
rewrite ler_pdivlMl 1?pmulr_lgt0// mulr1 ler_pdivlMl 1?pmulr_lgt0//.
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