X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fhelp%2FC%2Fsec_tactics.xml;h=364401aa5c7b130ded02950e6c72658fc3fb0543;hb=f583b4389d0227ff0da1954af484db7ef1f5fbfc;hp=56037dde56bf7d59f20b4efc6d6b1f848a2b643a;hpb=8752fac73a864c821b6954f0572bce2052924183;p=helm.git
diff --git a/helm/software/matita/help/C/sec_tactics.xml b/helm/software/matita/help/C/sec_tactics.xml
index 56037dde5..364401aa5 100644
--- a/helm/software/matita/help/C/sec_tactics.xml
+++ b/helm/software/matita/help/C/sec_tactics.xml
@@ -86,6 +86,61 @@
+
+ applyS
+ applyS
+ applyS t auto_params
+
+
+
+ Synopsis:
+
+ applyS &sterm; &autoparams;
+
+
+
+ Pre-conditions:
+
+ t must have type
+ T1 â ... â
+ Tn â G.
+
+
+
+ Action:
+
+ applyS is useful when
+ apply fails because the current goal
+ and the conclusion of the applied theorems are extensionally
+ equivalent up to instantiation of metavariables, but cannot
+ be unified. E.g. the goal is P(n*O+m) and
+ the theorem to be applied proves âm.P(m+O).
+
+
+ It tries to automatically rewrite the current goal using
+ auto paramodulation
+ to make it unifiable with G.
+ Then it closes the current sequent by applying
+ t to n
+ implicit arguments (that become new sequents).
+ The auto_params parameters are passed
+ directly to auto paramodulation.
+
+
+
+
+ New sequents to prove:
+
+ It opens a new sequent for each premise
+ Ti that is not
+ instantiated by unification. Ti is
+ the conclusion of the i-th new sequent to
+ prove.
+
+
+
+
+ assumptionassumption
@@ -123,13 +178,13 @@
autoauto
- auto depth=d width=w paramodulation full
+ auto paramsSynopsis:
- auto [depth=&nat;] [width=&nat;] [paramodulation] [full]
+ auto &autoparams;
@@ -137,10 +192,10 @@
None, but the tactic may fail finding a proof if every
proof is in the search space that is pruned away. Pruning is
- controlled by d and w.
+ controlled by the optional params.
Moreover, only lemmas whose type signature is a subset of the
signature of the current sequent are considered. The signature of
- a sequent is ...TODO
+ a sequent is ...&TODO;
@@ -160,6 +215,52 @@
+
+ cases
+ cases
+
+ cases t hyps
+
+
+
+
+ Synopsis:
+
+
+ cases
+ &term; [([&id;]â¦)]
+
+
+
+
+ Pre-conditions:
+
+
+ t must inhabit an inductive type
+
+
+
+
+ Action:
+
+
+ It proceed by cases on t. The new generated
+ hypothesis in each branch are named according to
+ hyps.
+
+
+
+
+ New sequents to prove:
+
+ One new sequent for each constructor of the type of
+ t. Each sequent has a new hypothesis for
+ each argument of the constructor.
+
+
+
+
+ clearclear
@@ -243,6 +344,58 @@
+
+ compose
+ compose
+ compose n t1 with t2 hyps
+
+
+
+ Synopsis:
+
+ compose [&nat;] &sterm; [with &sterm;] [&intros-spec;]
+
+
+
+ Pre-conditions:
+
+
+
+
+
+ Action:
+
+ Composes t1 with t2 in every possible way
+ n times introducing generated terms
+ as if intros hyps was issued.
+ If t1:âx:A.B[x] and
+ t2:âx,y:A.B[x]âB[y]âC[x,y] it generates:
+
+
+ λx,y:A.t2 x y (t1 x) : âx,y:A.B[y]âC[x,y]
+
+
+ λx,y:A.λH:B[x].t2 x y H (t1 y) : âx,y:A.B[x]âC[x,y]
+
+
+
+
+ If t2 is omitted it composes
+ t1
+ with every hypothesis that can be introduced.
+ n iterates the process.
+
+
+
+ New sequents to prove:
+
+ The same, but with more hypothesis eventually introduced
+ by the &intros-spec;.
+
+
+
+
+ changechange
@@ -395,8 +548,7 @@
decomposedecompose
- decompose (T1 ... Tn)
- H as H1 ... Hm
+ decompose as H1 ... Hm
@@ -405,10 +557,6 @@
decompose
- [(
- &id;â¦
- )]
- [&id;]
[as &id;â¦]
@@ -416,26 +564,22 @@
Pre-conditions:
-
- H must inhabit one inductive type among
-
- T1 ... Tn
-
- and the types of a predefined list.
-
+ None.Action:
- Runs
- elim H H1 ... Hm
- , clears H and tries to run itself
- recursively on each new identifier introduced by
+ For each each premise H of type
+ T in the current context where
+ T is a non-recursive inductive type without
+ right parameters and of sort Prop or CProp, the tactic runs
+
+ elim H as H1 ... Hm
+ , clears H and runs itself
+ recursively on each new premise introduced by
elim in the opened sequents.
- If H is not provided tries this operation on
- each premise in the current context.
@@ -483,30 +627,35 @@
-
- discriminate
- discriminate
- discriminate p
+
+ destruct
+ destruct
+ destruct pSynopsis:
- discriminate &sterm;
+ destruct &sterm;Pre-conditions:
- p must have type K t1 ... tn = K' t'1 ... t'm where K and K' must be different constructors of the same inductive type and each argument list can be empty if
-its constructor takes no arguments.
+ p must have type E1 = E2 where the two sides of the equality are possibly applied constructors of an inductive type.Action:
- It closes the current sequent by proving the absurdity of
- p.
+ The tactic recursively compare the two sides of the equality
+ looking for different constructors in corresponding position.
+ If two of them are found, the tactic closes the current sequent
+ by proving the absurdity of p. Otherwise
+ it adds a new hypothesis for each leaf of the formula that
+ states the equality of the subformulae in the corresponding
+ positions on the two sides of the equality.
+
@@ -897,43 +1046,6 @@ its constructor takes no arguments.
-
- injection
- injection
- injection p
-
-
-
- Synopsis:
-
- injection &sterm;
-
-
-
- Pre-conditions:
-
- p must have type K t1 ... tn = K t'1 ... t'n where both argument lists are empty if
-K takes no arguments.
-
-
-
- Action:
-
- It derives new hypotheses by injectivity of
- K.
-
-
-
- New sequents to prove:
-
- The new sequent to prove is equal to the current sequent
- with the additional hypotheses
- t1=t'1 ... tn=t'n.
-
-
-
-
- introintro
@@ -1232,39 +1344,6 @@ its constructor takes no arguments.
-
- paramodulation
- paramodulation
- paramodulation patt
-
-
-
- Synopsis:
-
- paramodulation &pattern;
-
-
-
- Pre-conditions:
-
- TODO.
-
-
-
- Action:
-
- TODO.
-
-
-
- New sequents to prove:
-
- TODO.
-
-
-
-
- reducereduce
@@ -1558,6 +1637,46 @@ its constructor takes no arguments.
+
+
+ subst
+ subst
+ subst
+
+
+
+ Synopsis:
+
+ subst
+
+
+
+ Pre-conditions:
+
+ None.
+
+
+
+ Action:
+
+ For each premise of the form
+ H: x = t or H: t = x
+ where x is a local variable and
+ t does not depend on x,
+ the tactic rewrites H wherever
+ x appears clearing H and
+ x afterwards.
+
+
+
+ New sequents to prove:
+
+ The one opened by the applied tactics.
+
+
+
+
+ symmetrysymmetry