diff options
| author | Georges Gonthier | 2019-11-22 10:02:04 +0100 |
|---|---|---|
| committer | Assia Mahboubi | 2019-11-22 10:02:04 +0100 |
| commit | 317267c618ecff861ec6539a2d6063cef298d720 (patch) | |
| tree | 8b9f3af02879faf1bba3ee9e7befcb52f44107ed /mathcomp/field/fieldext.v | |
| parent | b1ca6a9be6861f6c369db642bc194cf78795a66f (diff) | |
New generalised induction idiom (#434)
Replaced the legacy generalised induction idiom with a more robust one
that does not rely on the `{-2}` numerical occurrence selector, using
either new helper lemmas `ubnP` and `ltnSE` or a specific `nat`
induction principle `ltn_ind`.
Added (non-strict in)equality induction helper lemmas
Added `ubnP[lg]?eq` helper lemmas that abstract an integer expression
along with some (in)equality, in preparation for some generalised
induction. Note that while `ubnPleq` is very similar to `ubnP` (indeed
`ubnP M` is basically `ubnPleq M.+1`), `ubnPgeq` is used to remember
that the inductive value remains below the initial one.
Used the change log to give notice to users to update the generalised
induction idioms in their proofs to one of the new forms before
Mathcomp 1.11.
Diffstat (limited to 'mathcomp/field/fieldext.v')
| -rw-r--r-- | mathcomp/field/fieldext.v | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/mathcomp/field/fieldext.v b/mathcomp/field/fieldext.v index 64239f3..86d3d39 100644 --- a/mathcomp/field/fieldext.v +++ b/mathcomp/field/fieldext.v @@ -555,8 +555,8 @@ Qed. Lemma Fadjoin_sum_direct : directv sumKx. Proof. -rewrite directvE /=; case Dn: {-2}n (leqnn n) => // [m] {Dn}. -elim: m => [|m IHm] ltm1n; rewrite ?big_ord1 // !(big_ord_recr m.+1) /=. +rewrite directvE /=; case: (ubnPgeq n) (isT : n > 0) => -[//|m] ltmn _. +elim: m ltmn => [|m IHm] ltm1n; rewrite ?big_ord1 // !(big_ord_recr m.+1) /=. do [move/(_ (ltnW ltm1n))/eqP; set S := (\sum_i _)%VS] in IHm *. rewrite -IHm dimv_add_leqif; apply/subvP=> z; rewrite memv_cap => /andP[Sz]. case/memv_cosetP=> y Ky Dz; rewrite memv0 Dz mulf_eq0 expf_eq0 /=. |