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no errors hopefully

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This commit is contained in:
Egbert Rijke 2017-07-05 15:51:52 +01:00
parent 28b4559a0f
commit 997d75cbf3
2 changed files with 20 additions and 17 deletions
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32
homotopy/pointed_cubes.hlean
View file

@ -91,6 +91,9 @@ begin
exact (pconst_pcompose fleft)⁻¹*,
end
definition phsquare_of_ppi_homotopy {A B : Type*} {f g h i : A →* B} {phtpy_top : f ~* g} {phtpy_bot : h ~* i} {phtpy_left : f ~* h} {phtpy_right : g ~* i} (H : phtpy_top ⬝* phtpy_right ~~* phtpy_left ⬝* phtpy_bot) : phsquare phtpy_top phtpy_bot phtpy_left phtpy_right :=
eq_of_ppi_homotopy H
definition ptube_v {A B C D : Type*} {ftop ftop' : A →* B} (phtpy_top : ftop ~* ftop') {fbot fbot' : C →* D} (phtpy_bot : fbot ~* fbot') {fleft : A →* C} {fright : B →* D} (psq_back : psquare ftop fbot fleft fright) (psq_front : psquare ftop' fbot' fleft fright) : Type :=
phsquare (pwhisker_left fright phtpy_top) (pwhisker_right fleft phtpy_bot) psq_back psq_front
@ -122,20 +125,18 @@ structure p2homotopy {A B : Type*} {f g : A →* B} (H K : f ~* g) : Type :=
( to_2htpy : H ~ K)
( respect_pt : p2homotopy_ty_respect_pt to_2htpy)
definition phsquare_of_p2homotopy {A B : Type*} {f g h i : A →* B} {phtpy_top : f ~* g} {phtpy_bot : h ~* i} {phtpy_left : f ~* h} {phtpy_right : g ~* i} (p2htpy : (phtpy_top ⬝* phtpy_right) ~~* (phtpy_left ⬝* phtpy_bot)) : phsquare phtpy_top phtpy_bot phtpy_left phtpy_right :=
definition ptube_v_phtpy_bot {A B C D : Type*}
{ftop ftop' : A →* B} {phtpy_top : ftop ~* ftop'}
{fbot fbot' : C →* D} {phtpy_bot phtpy_bot' : fbot ~* fbot'} (ppi_htpy_bot : phtpy_bot ~~* phtpy_bot')
{fleft : A →* C} {fright : B →* D}
{psq_back : psquare ftop fbot fleft fright}
{psq_front : psquare ftop' fbot' fleft fright}
(ptb : ptube_v phtpy_top phtpy_bot psq_back psq_front)
: ptube_v phtpy_top phtpy_bot' psq_back psq_front
:=
begin
induction p2htpy,
induction phtpy_left using phomotopy_rec_on_idp,
induction phtpy_right using phomotopy_rec_on_idp,
induction to_2htpy, unfold phsquare,
repeat exact sorry
end
definition ptube_v_phtpy_bot {A B C D : Type*} {ftop ftop' : A →* B} {phtpy_top : ftop ~* ftop'} {fbot fbot' fbot'' : C →* D} {phtpy_bot : fbot ~* fbot'} {phtpy_bot' : fbot' ~* fbot''} {fleft : A →* C} {fright : B →* D} {psq_back : psquare ftop fbot fleft fright} {psq_front : psquare ftop' fbot' fleft fright} {psq_front' : psquare ftop' fbot'' fleft fright} (ptb : ptube_v phtpy_top phtpy_bot psq_back psq_front) (ptb' : ptube_v phomotopy.rfl phtpy_bot' psq_front psq_front') : ptube_v phtpy_top (phtpy_bot ⬝* phtpy_bot') psq_back psq_front' :=
begin
unfold ptube_v,
unfold phsquare,
repeat exact sorry
induction ppi_htpy_bot using ppi_homotopy_rec_on_idp,
exact ptb,
end
definition ptube_v_left_inv {A B C D : Type*} {ftop : A ≃* B} {fbot : C ≃* D} {fleft : A →* C} {fright : B →* D}
@ -146,5 +147,8 @@ definition ptube_v_left_inv {A B C D : Type*} {ftop : A ≃* B} {fbot : C ≃* D
(psquare_hcompose psq (psquare_inv_top_bot psq))
(psquare_of_pid_top_bot phomotopy.rfl) :=
begin
exact sorry
refine ptube_v_phtpy_bot _ _,
exact pleft_inv fbot,
exact ppi_homotopy.rfl,
fapply phsquare_of_ppi_homotopy, repeat exact sorry,
end

5
pointed_pi.hlean
View file

@ -168,9 +168,6 @@ namespace pointed
ppi_homotopy_of_eq (eq_of_ppi_homotopy h) = h :=
to_right_inv (ppi_eq_equiv k l) h
print pointed.phomotopy_rec_on_idp
print ppi_gen
variable (k)
definition eq_ppi_homotopy_refl_ppi_homotopy_of_eq_refl : ppi_homotopy.refl k = ppi_homotopy_of_eq (refl k) :=
@ -179,6 +176,8 @@ namespace pointed
induction p, reflexivity
end
variable {k}
definition ppi_homotopy_rec_on_eq [recursor] {k' : ppi_gen B x₀}
{Q : (k ~~* k') → Type} (p : k ~~* k') (H : Π(q : k = k'), Q (ppi_homotopy_of_eq q)) : Q p :=
ppi_homotopy_of_eq_of_ppi_homotopy p ▸ H (eq_of_ppi_homotopy p)