X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fhelp%2FC%2Fsec_declarative_tactics.xml;h=76acf5e0ad78a1bbfe3d6bb5333dd3b84ba2c9d2;hp=d77c276c4904db43fa894b2da9a3e29fa94da536;hb=784f0d4d7cff3700363affe647f7b8b218726fcb;hpb=8f699ab265e380a2d1ab7dba0ee5e8ba5556a84a diff --git a/matita/matita/help/C/sec_declarative_tactics.xml b/matita/matita/help/C/sec_declarative_tactics.xml index d77c276c4..76acf5e0a 100644 --- a/matita/matita/help/C/sec_declarative_tactics.xml +++ b/matita/matita/help/C/sec_declarative_tactics.xml @@ -1,5 +1,4 @@ - Action: - It proceeds by cases on t + It proceeds by case-analysis on t New sequents to prove: It opens one new sequent for each constructor of the - type of t. + type of t, each with the conclusion P instantiated for the constructor. - - - we proceed by induction on - we proceed by induction on - we proceed by induction on t to prove th - - - - Synopsis: - - we proceed by induction on &term; to prove &term; - - - - Pre-condition: - - t must inhabitant of an inductive type and - th must be the conclusion to be proved by induction. - - - - - Action: + + + case + case + case id (id1:T1) … (idn:Tn) + + + + Synopsis: + + case &id; [( &id; : &term; )] … [( &id; : &term; )] + + + + Pre-condition: - It proceed by induction on t. + The user must have started a proof by induction/cases that has not been concluded yet, id must be a constructor for the inductive type of the term under induction/case-analysis, and the case must not have already been proved. - - - New sequents to prove: + + + Action: - It opens one new sequent for each constructor of the - type of t. + It starts the proof for the case id, where id1:T1,…,idn:Tn are the arguments of the constructor, each declared with its type. - - - - + + + New sequents to prove: + + The sequent for the case id. + + + + + + + by induction hypothesis we know + by induction hypothesis we know + by induction hypothesis we know P (id) + + + + Synopsis: + by induction hypothesis we know &term; ( &id; ) + + + + Pre-condition: + + The user must have started proving a case for a proof by induction/case-analysis. + + + + Action: + + It introduces the inductive hypothesis. + + + + New sequents to prove: + + None. + + + + + - - we proved - we proved - justification we proved t (id) - - + + conclude + conclude + conclude t1 + + Synopsis: - &justification; we proved &term; - ( &id; - ) + conclude &term; + + + + Pre-condition: + + + The current conclusion must be an equality t1 = tk + + + + + Action: + + It starts an equality chain on the conclusion. It allows the user to apply the tactic = to continue the chain. - - - Pre-condition: + + + New sequent to prove: - tmust have type Prop. - + None. - - - Action: + + + + + + obtain + obtain + obtain H t1 + + + + Synopsis: + + obtain &id; &term; + + + + Pre-condition: - It derives t - using the justification and labels the conclusion with - id. - + + None. + + + + + Action: + + It starts an equality chain t1 = ?, which, when concluded, will be added to hypoteses of the current sequent. It allows the user to apply the tactic = to continue the chain. + + + + New sequent to prove: + + A new sequent for t1 = ? is opened, a new sequent for ? is opened, and a new sequent with the conclusion of the sequent on which this tactic was applied is opened, with H: t1 = ? added to its hypotheses. This hypotesis will be changed when the equality chain is concluded with H: t1 = tk, where tk is the last term of the equality chain. The goal for ? can be safely ignored, as it will be automatically closed when the equality chain is concluded. - - - New sequent to prove: + + + + + + = + = + = t2 justification + + + + Synopsis: + + + = &term; [&autoparams; | using &term; | using once &term; | proof] [done] + + + + + Pre-condition: - None. + + The user must have started an equality chain with conclude or obtain that has not been concluded yet. + + + + + Action: + + + It applies the transitivity of = on the left-hand-side of the current conclusion, t2, and the right-hand-side of the current conclusion, using the given justification. If done is supplied, this represents the last step in the equality chain. + + + + + New sequent to prove: + + + A new sequent for lhs = t2 is opened and then immediately closed using the given justification. A new sequent with the conclusion t2 = rhs is opened. + - - - - + + + + + + + done + done + justification done + + + + Synopsis: + + &justification; done + + + + Pre-condition: + + The user is proving a sequent which was opened with the tactic we need to prove, or the user is proving a sequent which was opened with the tactic we proceed by induction/cases on, or the user is proving a chain of equalities that was started with either the tactic conclude or obtain. + + + + Action: + + It closes the current sequent with the given justification. + + + + New sequents to prove: + + None. + + + + + --->