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Sophie Quinton
rtproofs
Commits
e4012a4d
Commit
e4012a4d
authored
Apr 05, 2017
by
Felipe Cerqueira
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Add tactic for splitting conjunction
parent
b6c93d38
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4
util/tactics.v
util/tactics.v
+36
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util/tactics.v
View file @
e4012a4d
...
...
@@ 403,8 +403,16 @@ Ltac exploit x :=

refine
((
fun
x
y
=>
y
x
)
(
x
_
_
)
_
)

refine
((
fun
x
y
=>
y
x
)
(
x
_
)
_
).
(* Feed tactic  exploit with multiple arguments.
(taken from http://comments.gmane.org/gmane.science.mathematics.logic.coq.club/7013) *)
(* This tactic feeds the precondition of an implication in order to derive the conclusion
(taken from http://comments.gmane.org/gmane.science.mathematics.logic.coq.club/7013).
Usage: feed H.
H: P > Q ==becomes==> H: P
____
Q
After completing this proof, Q becomes a hypothesis in the context. *)
Ltac
feed
H
:
=
match
type
of
H
with

?foo
>
_
=>
...
...
@@ 412,15 +420,39 @@ Ltac feed H :=
assert
foo
as
FOO
;
[
specialize
(
H
FOO
)
;
clear
FOO
]
end
.
(* Generalization of feed for multiple hypotheses.
feed_n is useful for accessing conclusions of long implications.
Usage: feed_n 3 H.
H: P1 > P2 > P3 > Q.
We'll be asked to prove P1, P2 and P3, so that Q can be inferred. *)
Ltac
feed_n
n
H
:
=
match
constr
:
(
n
)
with

O
=>
idtac

(
S
?m
)
=>
feed
H
;
[
feed_n
m
H
]
end
.
end
.
(* ************************************************************************** *)
(** * New tactics for ssreflect *)
(* ************************************************************************** *)
(* Tactic for simplifying a sum with constant term.
Usage: simpl_sum_const in H.
H: \sum_(2 <= x < 4) 5 > 0 ==becomes==> H: 5 * (4  2) > 0 *)
Ltac
simpl_sum_const
:
=
rewrite
?big_const_nat
?big_const_ord
?big_const_seq
iter_addn
?muln1
?mul1n
?mul0n
?muln0
?addn0
?add0n
.
\ No newline at end of file
?muln0
?addn0
?add0n
.
(* Tactic for splitting all conjunctions in a hypothesis.
Usage: split_conj H.
H: A /\ (B /\ C) ==becomes==> H1: A
H2: B
H3: C *)
Ltac
split_conj
X
:
=
hnf
in
X
;
repeat
match
goal
with

H
:
?p
/\
?q

_
=>
let
x'
:
=
H
in
let
y'
:
=
fresh
H
in
destruct
H
as
[
x'
y'
]
end
.
\ No newline at end of file
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