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Felipe Cerqueira
rt-proofs
Commits
e7d2a65b
Commit
e7d2a65b
authored
Dec 02, 2016
by
Felipe Cerqueira
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Add more lemmas about min/max
parent
d73b801d
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util/minmax.v
util/minmax.v
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util/minmax.v
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e7d2a65b
...
...
@@ -444,6 +444,17 @@ Section MinMaxSeq.
Definition
max_nat_cond
P
(
a
b
:
nat
)
:=
seq_max_nat
(
filter
P
(
values_between
a
b
)).
Lemma
min_nat_cond_exists
:
forall
(
P
:
nat
->
bool
)
(
a
b
:
nat
)
x
,
a
<=
x
<
b
->
P
x
->
min_nat_cond
P
a
b
!=
None
.
Proof
.
intros
P
a
b
x
LE
HOLDS
.
apply
seq_argmin_exists
with
(
x0
:=
x
).
by
rewrite
mem_filter
mem_values_between
HOLDS
LE
.
Qed
.
Lemma
min_nat_cond_in_seq
:
forall
P
a
b
x
,
min_nat_cond
P
a
b
=
Some
x
->
...
...
@@ -465,6 +476,17 @@ Section MinMaxSeq.
by
rewrite
mem_filter
Py
andTb
mem_values_between
.
Qed
.
Lemma
max_nat_cond_exists
:
forall
(
P
:
nat
->
bool
)
(
a
b
:
nat
)
x
,
a
<=
x
<
b
->
P
x
->
max_nat_cond
P
a
b
!=
None
.
Proof
.
intros
P
a
b
x
LE
HOLDS
.
apply
seq_argmax_exists
with
(
x0
:=
x
).
by
rewrite
mem_filter
mem_values_between
HOLDS
LE
.
Qed
.
Lemma
max_nat_cond_in_seq
:
forall
P
a
b
x
,
max_nat_cond
P
a
b
=
Some
x
->
...
...
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