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diff --git a/matita/help/C/sec_tactics.xml b/matita/help/C/sec_tactics.xml
index b4e3cb3a9..4bba23eb6 100644
--- a/matita/help/C/sec_tactics.xml
+++ b/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.
@@ -393,18 +393,21 @@ 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.
+ provided. If hyps specifies also a number of hypotheses that
+ is less than the number of new hypotheses for a new sequent,
+ then the exceeding hypothesis will be kept as implications in
+ the conclusion of the sequent.
- elimType <term> [using <term>]
+ elimType <term> [using <term>] [<intros_spec>]
elimType
- elimType T using th
+ elimType T using th hyps
@@ -437,20 +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.
@@ -465,7 +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.
@@ -473,13 +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.
@@ -496,13 +499,13 @@ its constructor takes no arguments.
Pre-conditions:
- none.
+ None.
Action:
- this tactic always fail.
+ This tactic always fail.
@@ -523,13 +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
@@ -540,7 +543,7 @@ its constructor takes no arguments.
New sequents to prove:
- none.
+ None.
@@ -555,7 +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.
@@ -564,13 +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.
@@ -612,21 +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
âx.G{x/t} where {x/t}
is a notation for the replacement with x of all
@@ -648,19 +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.
@@ -682,14 +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.
@@ -706,21 +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
@@ -748,14 +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.
@@ -776,14 +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.
@@ -791,7 +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"
@@ -838,7 +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.
@@ -846,13 +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.
@@ -869,20 +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 â t.
New sequents to prove:
- none.
+ None.
@@ -897,20 +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.
@@ -952,20 +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.
@@ -980,21 +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.
@@ -1009,13 +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.
@@ -1024,7 +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.
@@ -1048,7 +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
@@ -1059,7 +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.
@@ -1076,7 +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.
@@ -1084,13 +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.
@@ -1107,7 +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.
@@ -1115,7 +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).
@@ -1123,7 +1126,7 @@ its constructor takes no arguments.
New sequents to prove:
- none.
+ None.
@@ -1138,20 +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.
@@ -1166,7 +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.
@@ -1174,13 +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.
@@ -1198,20 +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.
@@ -1226,19 +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.
@@ -1255,13 +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
@@ -1272,7 +1275,7 @@ the current sequent to prove.
New sequents to prove:
- none.
+ None.
@@ -1287,20 +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.