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Sophie Quinton
rt-proofs
Commits
af7806cd
Commit
af7806cd
authored
Nov 02, 2016
by
Felipe Cerqueira
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Add new lemma about iter_fixpoint
parent
a5f12a43
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util/fixedpoint.v
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util/fixedpoint.v
View file @
af7806cd
...
...
@@ -124,6 +124,32 @@ Section Iteration.
}
Qed
.
(* We also show that any inductive property P is propagated
through the fixed-point iteration. *)
Lemma
iter_fixpoint_ind
:
forall
max_steps
x0
x
,
iter_fixpoint
max_steps
x0
=
Some
x
->
forall
P
,
P
x0
->
(
forall
x
,
P
x
->
P
(
f
x
))
->
P
x
.
Proof
.
induction
max_steps
;
first
by
done
.
intros
x0
x
SOME
P
P0
ALL
.
move
:
SOME
;
simpl
.
case
EQ
:
(
_
==
_
).
{
move
:
EQ
=>
/
eqP
EQ
.
case
=>
SAME
;
subst
.
by
rewrite
EQ
;
apply
ALL
.
}
{
intros
SOME
;
clear
EQ
.
apply
(
IHmax_steps
(
f
x0
)
x
SOME
P
)
;
first
by
apply
ALL
.
by
apply
ALL
.
}
Qed
.
End
BasicLemmas
.
Section
RelationLemmas
.
...
...
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