X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fhelp%2FC%2Fsec_tactics.xml;h=4bba23eb6e22c887d99171a63f6776f76dfdf4b5;hb=bfcb2bf3391de8f0c4de9b8d35ea44ddc71a4291;hp=6da46bd783d3c1b8eec012d3b66ddddc704d8de8;hpb=8048c0e5351ab5ac748d2b8d501fc64cdd69451f;p=helm.git diff --git a/helm/software/matita/help/C/sec_tactics.xml b/helm/software/matita/help/C/sec_tactics.xml index 6da46bd78..4bba23eb6 100644 --- a/helm/software/matita/help/C/sec_tactics.xml +++ b/helm/software/matita/help/C/sec_tactics.xml @@ -18,14 +18,14 @@ Action: - it closes the current sequent by eliminating an + It closes the current sequent by eliminating an absurd term. New sequents to prove: - it opens two new sequents of conclusion P + It opens two new sequents of conclusion P and ¬P. @@ -51,13 +51,13 @@ Action: - it closes the current sequent by applying t to n implicit arguments (that become new sequents). + It closes the current sequent by applying t to n implicit arguments (that become new sequents). New sequents to prove: - it opens a new sequent for each premise + 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 @@ -76,20 +76,20 @@ Pre-conditions: - there must exist an hypothesis whose type can be unified with + There must exist an hypothesis whose type can be unified with the conclusion of the current sequent. Action: - it closes the current sequent exploiting an hypothesis. + It closes the current sequent exploiting an hypothesis. New sequents to prove: - none + None @@ -104,7 +104,7 @@ Pre-conditions: - none, but the tactic may fail finding a proof if every + 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. Moreover, only lemmas whose type signature is a subset of the @@ -115,7 +115,7 @@ Action: - it closes the current sequent by repeated application of + It closes the current sequent by repeated application of rewriting steps (unless paramodulation is omitted), hypothesis and lemmas in the library. @@ -123,7 +123,7 @@ New sequents to prove: - none + None @@ -145,14 +145,14 @@ Action: - it hides the hypothesis H from the + It hides the hypothesis H from the current sequent. New sequents to prove: - none + None @@ -174,14 +174,14 @@ Action: - it hides the definiens of a definition in the current + It hides the definiens of a definition in the current sequent context. Thus the definition becomes an hypothesis. New sequents to prove: - none. + None. @@ -196,7 +196,7 @@ Pre-conditions: - each subterm matched by the pattern must be convertible + Each subterm matched by the pattern must be convertible with the term t disambiguated in the context of the matched subterm. @@ -204,7 +204,7 @@ Action: - it replaces the subterms of the current sequent matched by + It replaces the subterms of the current sequent matched by patt with the new term t. For each subterm matched by the pattern, t is disambiguated in the context of the subterm. @@ -213,7 +213,7 @@ New sequents to prove: - none. + None. @@ -228,7 +228,7 @@ Pre-conditions: - the conclusion of the current sequent must be + The conclusion of the current sequent must be an inductive type or the application of an inductive type with at least n constructors. @@ -236,14 +236,14 @@ Action: - it applies the n-th constructor of the + It applies the n-th constructor of the inductive type of the conclusion of the current sequent. New sequents to prove: - it opens a new sequent for each premise of the constructor + It opens a new sequent for each premise of the constructor that can not be inferred by unification. For more details, see the apply tactic. @@ -260,21 +260,21 @@ Pre-conditions: - there must be in the current context an hypothesis of type + There must be in the current context an hypothesis of type False. Action: - it closes the current sequent by applying an hypothesis of + It closes the current sequent by applying an hypothesis of type False. New sequents to prove: - none + None @@ -295,13 +295,13 @@ Action: - it closes the current sequent. + It closes the current sequent. New sequents to prove: - it opens two new sequents. The first one has an extra + It opens two new sequents. The first one has an extra hypothesis H:P. If H is omitted, the name of the hypothesis is automatically generated. The second sequent has conclusion P and @@ -354,14 +354,14 @@ its constructor takes no arguments. Action: - it closes the current sequent by proving the absurdity of + It closes the current sequent by proving the absurdity of p. New sequents to prove: - none. + None. @@ -385,7 +385,7 @@ its constructor takes no arguments. Action: - it proceeds by cases on the values of t, + It proceeds by cases on the values of t, according to the elimination principle th. @@ -393,7 +393,7 @@ its constructor takes no arguments. New sequents to prove: - it opens one new sequent for each case. The names of + It opens one new sequent for each case. The names of the new hypotheses are picked by hyps, if provided. If hyps specifies also a number of hypotheses that is less than the number of new hypotheses for a new sequent, @@ -440,20 +440,20 @@ its constructor takes no arguments. Pre-conditions: - the type of p must be convertible + The type of p must be convertible with the conclusion of the current sequent. Action: - it closes the current sequent using p. + It closes the current sequent using p. New sequents to prove: - none. + None. @@ -468,7 +468,7 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current sequent must be + The conclusion of the current sequent must be an inductive type or the application of an inductive type with at least one constructor. @@ -476,13 +476,13 @@ its constructor takes no arguments. Action: - equivalent to constructor 1. + Equivalent to constructor 1. New sequents to prove: - it opens a new sequent for each premise of the first + It opens a new sequent for each premise of the first constructor of the inductive type that is the conclusion of the current sequent. For more details, see the constructor tactic. @@ -499,13 +499,13 @@ its constructor takes no arguments. Pre-conditions: - none. + None. Action: - this tactic always fail. + This tactic always fail. @@ -526,13 +526,13 @@ its constructor takes no arguments. Pre-conditions: - the pattern must not specify the wanted term. + The pattern must not specify the wanted term. Action: - first of all it locates all the subterms matched by + First of all it locates all the subterms matched by patt. In the context of each matched subterm it disambiguates the term t and reduces it to its red normal form; then it replaces with @@ -543,7 +543,7 @@ its constructor takes no arguments. New sequents to prove: - none. + None. @@ -558,7 +558,7 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current sequent must be a linear + The conclusion of the current sequent must be a linear inequation over real numbers taken from standard library of Coq. Moreover the inequations in the hypotheses must imply the inequation in the conclusion of the current sequent. @@ -567,13 +567,13 @@ its constructor takes no arguments. Action: - it closes the current sequent by applying the Fourier method. + It closes the current sequent by applying the Fourier method. New sequents to prove: - none. + None. @@ -615,21 +615,21 @@ its constructor takes no arguments. Pre-conditions: - all the terms matched by patt must be + All the terms matched by patt must be convertible and close in the context of the current sequent. Action: - it closes the current sequent by applying a stronger + It closes the current sequent by applying a stronger lemma that is proved using the new generated sequent. New sequents to prove: - it opens a new sequent where the current sequent conclusion + It opens a new sequent where the current sequent conclusion G is generalized to ∀x.G{x/t} where {x/t} is a notation for the replacement with x of all @@ -651,19 +651,19 @@ its constructor takes no arguments. Pre-conditions: - none. + None. Action: - this identity tactic does nothing without failing. + This identity tactic does nothing without failing. New sequents to prove: - none. + None. @@ -685,14 +685,14 @@ its constructor takes no arguments. Action: - it derives new hypotheses by injectivity of + It derives new hypotheses by injectivity of K. New sequents to prove: - the new sequent to prove is equal to the current sequent + The new sequent to prove is equal to the current sequent with the additional hypotheses t1=t'1 ... tn=t'n. @@ -709,21 +709,21 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the sequent to prove must be an implication + The conclusion of the sequent to prove must be an implication or a universal quantification. Action: - it applies the right introduction rule for implication, + It applies the right introduction rule for implication, closing the current sequent. New sequents to prove: - it opens a new sequent to prove adding to the hypothesis + It opens a new sequent to prove adding to the hypothesis the antecedent of the implication and setting the conclusion to the consequent of the implicaiton. The name of the new hypothesis is H if provided; otherwise it @@ -751,14 +751,14 @@ its constructor takes no arguments. Action: - it applies several times the right introduction rule for + It applies several times the right introduction rule for implication, closing the current sequent. New sequents to prove: - it opens a new sequent to prove adding a number of new + It opens a new sequent to prove adding a number of new hypotheses equal to the number of new hypotheses requested. If the user does not request a precise number of new hypotheses, it adds as many hypotheses as possible. @@ -779,14 +779,14 @@ its constructor takes no arguments. Pre-conditions: - the type of the term t must be an inductive + The type of the term t must be an inductive type or the application of an inductive type. Action: - it proceeds by cases on t paying attention + It proceeds by cases on t paying attention to the constraints imposed by the actual "right arguments" of the inductive type. @@ -794,7 +794,7 @@ its constructor takes no arguments. New sequents to prove: - it opens one new sequent to prove for each case in the + It opens one new sequent to prove for each case in the definition of the type of t. With respect to a simple elimination, each new sequent has additional hypotheses that states the equalities of the "right parameters" @@ -841,7 +841,7 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current sequent must be + The conclusion of the current sequent must be an inductive type or the application of an inductive type with at least one constructor. @@ -849,13 +849,13 @@ its constructor takes no arguments. Action: - equivalent to constructor 1. + Equivalent to constructor 1. New sequents to prove: - it opens a new sequent for each premise of the first + It opens a new sequent for each premise of the first constructor of the inductive type that is the conclusion of the current sequent. For more details, see the constructor tactic. @@ -872,20 +872,20 @@ its constructor takes no arguments. Pre-conditions: - none. + None. Action: - it adds to the context of the current sequent to prove a new + It adds to the context of the current sequent to prove a new definition x ≝ t. New sequents to prove: - none. + None. @@ -900,20 +900,20 @@ its constructor takes no arguments. Pre-conditions: - none. + None. Action: - it replaces all the terms matched by patt + It replaces all the terms matched by patt with their βδιζ-normal form. New sequents to prove: - none. + None. @@ -955,20 +955,20 @@ its constructor takes no arguments. Pre-conditions: - none. + None. Action: - it replaces all the terms matched by patt + It replaces all the terms matched by patt with their βδιζ-normal form. New sequents to prove: - none. + None. @@ -983,21 +983,21 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current sequent must be + The conclusion of the current sequent must be t=t for some term t Action: - it closes the current sequent by reflexivity + It closes the current sequent by reflexivity of equality. New sequents to prove: - none. + None. @@ -1012,13 +1012,13 @@ its constructor takes no arguments. Pre-conditions: - none. + None. Action: - it replaces the subterms of the current sequent matched by + It replaces the subterms of the current sequent matched by patt with the new term t. For each subterm matched by the pattern, t is disambiguated in the context of the subterm. @@ -1027,7 +1027,7 @@ its constructor takes no arguments. New sequents to prove: - for each matched term t' it opens + For each matched term t' it opens a new sequent to prove whose conclusion is t'=t. @@ -1051,7 +1051,7 @@ its constructor takes no arguments. Action: - it looks in every term matched by patt + It looks in every term matched by patt for all the occurrences of the left hand side of the equality that p proves (resp. the right hand side if dir is @@ -1062,7 +1062,7 @@ its constructor takes no arguments. New sequents to prove: - it opens one new sequent for each hypothesis of the + It opens one new sequent for each hypothesis of the equality proved by p that is not closed by unification. @@ -1079,7 +1079,7 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current sequent must be + The conclusion of the current sequent must be an inductive type or the application of an inductive type with at least two constructors. @@ -1087,13 +1087,13 @@ its constructor takes no arguments. Action: - equivalent to constructor 2. + Equivalent to constructor 2. New sequents to prove: - it opens a new sequent for each premise of the second + It opens a new sequent for each premise of the second constructor of the inductive type that is the conclusion of the current sequent. For more details, see the constructor tactic. @@ -1110,7 +1110,7 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current sequent must be an + The conclusion of the current sequent must be an equality over Coq's real numbers that can be proved using the ring properties of the real numbers only. @@ -1118,7 +1118,7 @@ its constructor takes no arguments. Action: - it closes the current sequent veryfying the equality by + It closes the current sequent veryfying the equality by means of computation (i.e. this is a reflexive tactic, implemented exploiting the "two level reasoning" technique). @@ -1126,7 +1126,7 @@ its constructor takes no arguments. New sequents to prove: - none. + None. @@ -1141,20 +1141,20 @@ its constructor takes no arguments. Pre-conditions: - none. + None. Action: - it replaces all the terms matched by patt + It replaces all the terms matched by patt with other convertible terms that are supposed to be simpler. New sequents to prove: - none. + None. @@ -1169,7 +1169,7 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current sequent must be + The conclusion of the current sequent must be an inductive type or the application of an inductive type with at least one constructor. @@ -1177,13 +1177,13 @@ its constructor takes no arguments. Action: - equivalent to constructor 1. + Equivalent to constructor 1. New sequents to prove: - it opens a new sequent for each premise of the first + It opens a new sequent for each premise of the first constructor of the inductive type that is the conclusion of the current sequent. For more details, see the constructor tactic. @@ -1201,20 +1201,20 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current proof must be an equality. + The conclusion of the current proof must be an equality. Action: - it swaps the two sides of the equalityusing the symmetric + It swaps the two sides of the equalityusing the symmetric property. New sequents to prove: - none. + None. @@ -1229,19 +1229,19 @@ its constructor takes no arguments. Pre-conditions: - the conclusion of the current proof must be an equality. + The conclusion of the current proof must be an equality. Action: - it closes the current sequent by transitivity of the equality. + It closes the current sequent by transitivity of the equality. New sequents to prove: - it opens two new sequents l=t and + It opens two new sequents l=t and t=r where l and r are the left and right hand side of the equality in the conclusion of the current sequent to prove. @@ -1258,13 +1258,13 @@ the current sequent to prove. Pre-conditions: - none. + None. Action: - it finds all the occurrences of t + It finds all the occurrences of t (possibly applied to arguments) in the subterms matched by patt. Then it δ-expands each occurrence, also performing β-reduction of the obtained term. If @@ -1275,7 +1275,7 @@ the current sequent to prove. New sequents to prove: - none. + None. @@ -1290,20 +1290,20 @@ the current sequent to prove. Pre-conditions: - none. + None. Action: - it replaces all the terms matched by patt + It replaces all the terms matched by patt with their βδιζ-weak-head normal form. New sequents to prove: - none. + None.