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| -rw-r--r-- | doc/sphinx/proof-engine/ssreflect-proof-language.rst | 39 |
1 files changed, 19 insertions, 20 deletions
diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst index 52609546d5..3ca0ffe678 100644 --- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst +++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst @@ -916,11 +916,8 @@ but also folds ``x`` in the goal. .. coqtop:: reset From Coq Require Import ssreflect. - Set Implicit Arguments. - Unset Strict Implicit. - Unset Printing Implicit Defensive. - .. coqtop:: all undo + .. coqtop:: all Lemma test x t (Hx : x = 3) : x + t = 4. set z := 3 in Hx. @@ -929,6 +926,10 @@ If the localization also mentions the goal, then the result is the following one .. example:: + .. coqtop:: reset + + From Coq Require Import ssreflect. + .. coqtop:: all Lemma test x t (Hx : x = 3) : x + t = 4. @@ -2485,8 +2486,7 @@ destruction of existential assumptions like in the tactic: .. coqtop:: all Lemma test : True. - have [x Px]: exists x : nat, x > 0. - Focus 2. + have [x Px]: exists x : nat, x > 0; last first. An alternative use of the ``have`` tactic is to provide the explicit proof term for the intermediate lemma, using tactics of the form: @@ -2564,8 +2564,7 @@ copying the goal itself. .. coqtop:: all Lemma test : True. - have suff H : 2 + 2 = 3. - Focus 2. + have suff H : 2 + 2 = 3; last first. Note that H is introduced in the second goal. @@ -2852,8 +2851,7 @@ pattern will be used to process its instance. .. coqtop:: all Lemma simple n (ngt0 : 0 < n ) : P n. - gen have ltnV, /andP[nge0 neq0] : n ngt0 / (0 <= n) && (n != 0). - Focus 2. + gen have ltnV, /andP[nge0 neq0] : n ngt0 / (0 <= n) && (n != 0); last first. .. _advanced_generalization_ssr: @@ -3556,6 +3554,7 @@ corresponding new goals will be generated. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. + Set Warnings "-notation-overridden". .. coqtop:: all @@ -3756,9 +3755,10 @@ which the function is supplied: :name: congr This tactic: -+ checks that the goal is a Leibniz equality -+ matches both sides of this equality with “term applied to some arguments”, inferring the right number of arguments from the goal and the type of term. This may expand some definitions or fixpoints. -+ generates the subgoals corresponding to pairwise equalities of the arguments present in the goal. + + + checks that the goal is a Leibniz equality; + + matches both sides of this equality with “term applied to some arguments”, inferring the right number of arguments from the goal and the type of term. This may expand some definitions or fixpoints; + + generates the subgoals corresponding to pairwise equalities of the arguments present in the goal. The goal can be a non dependent product ``P -> Q``. In that case, the system asserts the equation ``P = Q``, uses it to solve the goal, and @@ -4918,7 +4918,7 @@ which produces the converse implication. In both cases, the two first Prop arguments are implicit. If ``term`` is an instance of the ``reflect`` predicate, then ``A`` will be one -of the defined view hints for the ``reflec``t predicate, which are by +of the defined view hints for the ``reflect`` predicate, which are by default the ones present in the file ``ssrbool.v``. These hints are not only used for choosing the appropriate direction of the translation, but they also allow complex transformation, involving negations. @@ -4933,9 +4933,9 @@ but they also allow complex transformation, involving negations. Unset Printing Implicit Defensive. Section Test. - .. coqtop:: in + .. coqtop:: all - Lemma introN : forall (P : Prop) (b : bool), reflect P b -> ~ P -> ~~b. + Check introN. .. coqtop:: all @@ -4945,12 +4945,11 @@ but they also allow complex transformation, involving negations. In fact this last script does not exactly use the hint ``introN``, but the more general hint: - .. coqtop:: in + .. coqtop:: all - Lemma introNTF : forall (P : Prop) (b c : bool), - reflect P b -> (if c then ~ P else P) -> ~~ b = c. + Check introNTF. - The lemma ` `introN`` is an instantiation of introNF using c := true. + The lemma ``introN`` is an instantiation of ``introNF`` using ``c := true``. Note that views, being part of :token:`i_pattern`, can be used to interpret assertions too. For example the following script asserts ``a && b`` but |