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Pierre Letouzey
natded
Commits
a530466b
Commit
a530466b
authored
Jun 30, 2020
by
Samuel Ben Hamou
Browse files
Recorrection des dépendances circulaires (mauvais revert...)
parent
c9783d14
Changes
2
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Side-by-side
Peano.v
View file @
a530466b
...
...
@@ -279,8 +279,15 @@ Proof.
apply
R_All_e
with
(
t
:=
Succ
(
FVar
"y"
))
in
AX10
;
auto
.
Qed
.
Lemma
Comm
:
IsTheorem
Intuiti
PeanoTheory
(
∀∀
(#
0
+
#
1
=
#
1
+
#
0
)).
Admitted
.
Lemma
Comm
:
IsTheorem
Intuiti
PeanoTheory
(
∀
(#
0
=
#
0
+
Zero
)
->
∀∀
(
Succ
(#
1
+
#
0
)
=
#
1
+
Succ
(#
0
))
->
∀∀
(#
0
+
#
1
=
#
1
+
#
0
)).
Proof
.
assert
(
IsTheorem
Intuiti
PeanoTheory
(
∀
(#
0
=
#
0
+
Zero
))
->
IsTheorem
Intuiti
PeanoTheory
(
∀∀
(
Succ
(#
1
+
#
0
)
=
#
1
+
Succ
(#
0
))
->
∀∀
(#
0
+
#
1
=
#
1
+
#
0
))
->
IsTheorem
Intuiti
PeanoTheory
(
∀
(#
0
=
#
0
+
Zero
)
->
∀∀
(
Succ
(#
1
+
#
0
)
=
#
1
+
Succ
(#
0
))
->
∀∀
(#
0
+
#
1
=
#
1
+
#
0
))).
{
apply
ModusPonens
.
}
apply
ModusPonens
with
(
A
:=
∀
(#
0
=
#
0
+
Zero
)).
(
**
A
Coq
model
of
this
Peano
theory
,
based
on
the
[
nat
]
type
*
)
...
...
Theories.v
View file @
a530466b
...
...
@@ -4,7 +4,7 @@
(
**
The
NatDed
development
,
Pierre
Letouzey
,
2019.
This
file
is
released
under
the
CC0
License
,
see
the
LICENSE
file
*
)
Require
Import
Defs
NameProofs
Mix
Meta
Countable
Models
.
Require
Import
Defs
NameProofs
Mix
Meta
Countable
.
Import
ListNotations
.
Local
Open
Scope
bool_scope
.
Local
Open
Scope
eqb_scope
.
...
...
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