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- Rename `eq_sorted` lemmas to `sorted_eq` to address a naming inconsistency.
- Lemma `sort_le_id` has been generalized from `orderType` to `porderType`.
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This change reduces
- use of numerical occurrence selectors (#436) and
- use of non ssreflect tactics such as `auto`,
and improves use of comparison predicates such as `posnP`, `leqP`, `ltnP`,
`ltngtP`, and `eqVneq`.
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- Replace `altP eqP` and `altP (_ =P _)` with `eqVneq`:
The improved `eqVneq` lemma (#351) is redesigned as a comparison predicate and
introduces a hypothesis in the form of `x != y` in the second case. Thus,
`case: (altP eqP)`, `case: (altP (x =P _))` and `case: (altP (x =P y))` idioms
can be replaced with `case: eqVneq`, `case: (eqVneq x)` and
`case: (eqVneq x y)` respectively. This replacement slightly simplifies and
reduces proof scripts.
- use `have [] :=` rather than `case` if it is better.
- `by apply:` -> `exact:`.
- `apply/lem1; apply/lem2` or `apply: lem1; apply: lem2` -> `apply/lem1/lem2`.
- `move/lem1; move/lem2` -> `move/lem1/lem2`.
- Remove `GRing.` prefix if applicable.
- `negbTE` -> `negPf`, `eq_refl` -> `eqxx` and `sym_equal` -> `esym`.
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Added lemmas `big_enum_cond`, `big_enum` and `big_enumP` to handle more
explicitly big ops iterating over explicit enumerations in a `finType`.
The previous practice was to rely on the convertibility between
`enum A` and `filter A (index_enum T)`, sometimes explicitly via the
`filter_index_enum` equality, more often than not implicitly.
Both are likely to fail after the integration of `finmap`, as the
`choiceType` theory can’t guarantee that the order in selected
enumerations is consistent.
For this reason `big_enum` and the related (but currently unused)
`big_image` lemmas are restricted to the abelian case. The `big_enumP`
lemma can be used to handle enumerations in the non-abelian case, as
explained in the `bigop.v` internal documentation.
The Changelog entry enjoins clients to stop relying on either
`filter_index_enum` and convertibility (though this PR still provides
both), and warns about the restriction of the `big_image` lemma set to
the abelian case, as it it a possible source of incompatibility.
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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.
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Thanks!
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Construct `finfun_of` directly from a bespoke indexed inductive type,
which both makes it structurally positive (and therefore usable as a
container in an `Inductive` definition), and accommodates naturally
dependent functions.
This is still WIP, because this PR exposed a serious shortcoming of
the Coq unification algorithm’s implantation of Miller patterns. This
bug defeats the inference of `Canonical` structures for `{ffun S -> T}`
when the instances are defined in the dependent case!
This causes unmanageable regressions starting in `matrix.v`, so I
have not been able to check for any impact past that. I’m pushing this
commit so that the Coq issue may be addressed.
Made `fun_of_fin` structurally decreasing: Changed the primitive
accessor of `finfun_of` from `tfgraph` to the `Funclass` coercion
`fun_of_fin`. This will make it possible to define recursive functions
on inductive types built using finite functions. While`tfgraph` is
still useful to transport the tuple canonical structures to
`finfun_of`, it is no longer central to the theory so its role has
been reduced.
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Variable renaming from 'C(m,n) to 'C(n,m)
Renaming theorem mul_Sm_binn to mul_bin_diag
Adding theorems mul_bin_left mul_bin_right
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