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Micaela Mayero
Numerical Analysis in Coq
Commits
63a2afb3
Commit
63a2afb3
authored
1 week ago
by
François Clément
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Add am_lm_equiv_ms,
fct_lm_gather_ms, am_gather{_equiv,,_rev}_ms (proofs redone, why?)
parent
340678d8
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Stage: deploy
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Algebra/AffineSpace/AffineSpace_aff_map.v
+25
-9
25 additions, 9 deletions
Algebra/AffineSpace/AffineSpace_aff_map.v
with
25 additions
and
9 deletions
Algebra/AffineSpace/AffineSpace_aff_map.v
+
25
−
9
View file @
63a2afb3
...
...
@@ -689,6 +689,10 @@ Lemma am_normal_rev_ms :
sum
L
=
1
->
f
(
barycenter_ms
L
A1
)
=
barycenter_ms
L
(
mapF
f
A1
).
Proof
.
intro
;
apply
am_normal_rev
.
Qed
.
Lemma
am_lm_equiv_ms
:
forall
{
f
:
E1
->
E2
}
O1
,
aff_map_ms
f
<->
lin_map
(
fct_lm_ms
f
O1
).
Proof
.
intro
;
apply
am_lm_equiv
.
Qed
.
Lemma
lm_am
:
forall
{
f
:
E1
->
E2
}
,
lin_map
f
->
aff_map_ms
f
.
Proof
.
intros
;
apply
am_lm_0
;
apply
lm_fct_minus
;
...
...
@@ -708,19 +712,31 @@ Lemma am_comp_ms :
aff_map_ms
f12
->
aff_map_ms
f23
->
aff_map_ms
(
f23
\
o
f12
).
Proof
.
move
=>>
;
apply
am_comp
.
Qed
.
Lemma
am_gather_rev_ms
:
(
*
FIXME
:
COMMENTS
TO
BE
REMOVED
FOR
PUBLICATION
!
TODO
FC
(
07
/
03
/
2025
)
:
understand
why
we
have
to
redo
the
following
proofs
.
*
)
Lemma
fct_lm_gather_ms
:
forall
{
n
}
(
f
:
'
(
E1
->
E2
)
^
n
)
O1
,
fct_lm_ms
(
gather
f
)
O1
=
gather
(
fun
i
=>
fct_lm_ms
(
f
i
)
O1
).
Proof
.
easy
.
Qed
.
Lemma
am_gather_equiv_ms
:
forall
{
n
}
(
f
:
'
(
E1
->
E2
)
^
n
),
aff_map_ms
(
gather
f
)
->
forall
i
,
aff_map_ms
(
f
i
).
aff_map_ms
(
gather
f
)
<
->
(
forall
i
,
aff_map_ms
(
f
i
)
)
.
Proof
.
move
=>>
Hf
;
apply
am_gather_rev
=>>
HL
;
extF
i
;
rewrite
Hf
//.
move:
i
;
apply
extF_rev
.
intros
n
f
;
pose
(
O1
:=
point_of_as
E1
).
rewrite
(
am_lm_equiv_ms
O1
)
fct_lm_gather_ms
lm_gather_equiv
.
apply
equiv_forall
;
intro
;
rewrite
am_lm_equiv_ms
;
easy
.
Qed
.
Lemma
am_gather_ms
:
forall
{
n
}
(
f
:
'
(
E1
->
E2
)
^
n
),
(
forall
i
,
aff_map_ms
(
f
i
))
->
aff_map_ms
(
gather
f
).
Proof
.
move
=>>
;
apply
am_gather_equiv_ms
.
Qed
.
Admitted
.
Lemma
am_gather_rev_ms
:
forall
{
n
}
(
f
:
'
(
E1
->
E2
)
^
n
),
aff_map_ms
(
gather
f
)
->
forall
i
,
aff_map_ms
(
f
i
).
Proof
.
move
=>>
;
apply
am_gather_equiv_ms
.
Qed
.
End
ModuleSpace_AffineSpace_Morphism_Facts2
.
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