diff options
| author | Cyril Cohen | 2017-12-12 18:41:31 +0100 |
|---|---|---|
| committer | Cyril Cohen | 2017-12-12 19:34:58 +0100 |
| commit | f0c46d647c7f5c7dc88cb2b06d20ea92ae2f9da1 (patch) | |
| tree | 71f2f194d921c7d9e12db0fde44011a38d91a14f /mathcomp | |
| parent | 051a83a5f1efcf1a06f7ab0456dc6ffeb8d168e3 (diff) | |
refactored proof and renamed to reshape_leq and removed spurious hypothesis
Diffstat (limited to 'mathcomp')
| -rw-r--r-- | mathcomp/ssreflect/seq.v | 22 |
1 files changed, 9 insertions, 13 deletions
diff --git a/mathcomp/ssreflect/seq.v b/mathcomp/ssreflect/seq.v index d562f25..5574892 100644 --- a/mathcomp/ssreflect/seq.v +++ b/mathcomp/ssreflect/seq.v @@ -2623,21 +2623,17 @@ elim: ss => //= s ss IHss in i *; rewrite subn_eq0 nth_cat. by have [//|le_s_i] := ltnP; rewrite subnDA subSn /=. Qed. -Lemma reshape_index_leq sh i1 i2 - (r1 := reshape_index sh i1) (c1 := reshape_offset sh i1) - (r2 := reshape_index sh i2) (c2 := reshape_offset sh i2) : - i2 < sumn sh -> - (i1 <= i2) = ((r1 < r2) || ((r1 == r2 ) && (c1 <= c2))). +Lemma reshape_leq sh i1 i2 + (r1 := reshape_index sh i1) (c1 := reshape_offset sh i1) + (r2 := reshape_index sh i2) (c2 := reshape_offset sh i2) : + (i1 <= i2) = ((r1 < r2) || ((r1 == r2) && (c1 <= c2))). Proof. rewrite {}/r1 {}/c1 {}/r2 {}/c2 /reshape_offset /reshape_index. -elim: sh i1 i2 => [i1 i2 |] //= s0 s IHs i1 i2. -rewrite !subn_eq0. -case: (ltnP i1 s0) => Hi1s0 //= ; case: (ltnP i2 s0) => Hi2s0 //=. -- by rewrite !subn0. -- by have := leq_trans Hi1s0 Hi2s0 => /ltnW ->. -- by have := leq_trans Hi2s0 Hi1s0; rewrite ltnNge => /negbTE ->. -- rewrite -leq_subLR ltnS eqSS (subSn Hi1s0) (subSn Hi2s0). - by rewrite -{2}(subnK Hi2s0) addnC -leq_subLR !subnDA => /IHs ->. +elim: sh => [|s0 s IHs] /= in i1 i2 *; rewrite ?subn0 ?subn_eq0 //. +have [[] i1s0 [] i2s0] := (ltnP i1 s0, ltnP i2 s0); first by rewrite !subn0. +- by apply: leq_trans i2s0; apply/ltnW. +- by apply/negP => /(leq_trans i1s0); rewrite leqNgt i2s0. +by rewrite !subSn // !eqSS !ltnS !subnDA -IHs leq_subLR subnKC. Qed. End Flatten. |