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Pierre Letouzey
natded
Commits
13ff6682
Commit
13ff6682
authored
Jul 16, 2020
by
Samuel Ben Hamou
Browse files
Debut preuve emptyset.
parent
9e00370c
Changes
2
Hide whitespace changes
Inline
Side-by-side
Mix.v
View file @
13ff6682
...
...
@@ -226,7 +226,6 @@ Fixpoint lift t :=
end
.
(
*
+
1
sur
les
dB
>=
k
*
)
Fixpoint
lift_above
k
t
:=
match
t
with
|
BVar
n
=>
if
(
k
<=?
n
)
%
nat
then
BVar
(
S
n
)
else
t
...
...
ZF.v
View file @
13ff6682
...
...
@@ -208,10 +208,28 @@ End ZFAx.
Local
Open
Scope
string
.
Local
Open
Scope
formula_scope
.
Definition
ZF
Theory
:=
Definition
ZF
:=
{|
sign
:=
ZFSign
;
IsAxiom
:=
ZFAx
.
IsAx
;
WfAxiom
:=
ZFAx
.
WfAx
|}
.
Import
ZFAx
.
Import
ZFAx
.
\ No newline at end of file
Ltac
thm
:=
unfold
IsTheorem
;
split
;
[
unfold
Wf
;
split
;
[
auto
|
split
;
auto
]
|
].
Lemma
emptyset
:
IsTheorem
Intuiti
ZF
(
∃∀
~
(#
0
∈
#
1
)).
Proof
.
thm
.
exists
[
infinity
].
split
;
auto
.
-
simpl
.
rewrite
Forall_forall
.
intros
.
destruct
H
.
+
rewrite
<-
H
.
unfold
IsAx
.
left
.
compute
;
intuition
.
+
inversion
H
.
-
apply
R_Ex_e
with
(
A
:=
infinity
)
(
x
:=
"a"
).
+
intro
.
cbn
in
H
.
Lemma
singleton
:
IsTheorem
Intuiti
ZF
(
∀∃∀
(#
0
∈
#
1
<->
#
0
=
#
2
)).
Admitted
.
Lemma
union
:
IsTheorem
Intuiti
ZF
(
∀∀∃∀
(#
0
∈
#
1
<->
#
0
∈
#
2
\
/
#
0
∈
#
3
)).
Admitted
.
\ No newline at end of file
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