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further reductions to pointed_pi

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This commit is contained in:
Egbert Rijke 2017-07-08 14:49:32 +01:00
parent b8bb1ca67d
commit 1c51df13f2
1 changed files with 17 additions and 2 deletions
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19
homotopy/spectrum.hlean
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@ -698,6 +698,20 @@ set_option pp.coercions true
intro a, exact glue_square (f a) n, intro a, exact glue_square (f a) n,
end end
definition psquare_loop_ppi_compose_left {A : Type*} {X Y : A → Type*} (f : Π (a : A), X a →* Y a) :
psquare
(Ω→ (ppi_compose_left f))
(ppi_compose_left (λ a, Ω→ (f a)))
(ppi_loop_pequiv)
(ppi_loop_pequiv)
:=
begin
fapply psquare_of_phomotopy,
fapply phomotopy.mk, intro g,
fapply eq_of_ppi_homotopy, fapply ppi_homotopy.mk, intro a,
repeat exact sorry
end /- TODO FOR SSS -/
definition spi_compose_left_botsq definition spi_compose_left_botsq
{N : succ_str} {A : Type*} {E F : A → gen_spectrum N} (f : Π a, (E a) →ₛ (F a)) (n : N) {N : succ_str} {A : Type*} {E F : A → gen_spectrum N} (f : Π a, (E a) →ₛ (F a)) (n : N)
: psquare : psquare
@ -707,8 +721,9 @@ set_option pp.coercions true
(pequiv.to_pmap ppi_loop_pequiv⁻¹ᵉ*) (pequiv.to_pmap ppi_loop_pequiv⁻¹ᵉ*)
:= :=
begin begin
exact sorry refine (_)⁻¹ᵛ*,
end /- TODO FOR SSS -/ fapply psquare_loop_ppi_compose_left,
end
definition spi_compose_left [constructor] {N : succ_str} {A : Type*} {E F : A -> gen_spectrum N} definition spi_compose_left [constructor] {N : succ_str} {A : Type*} {E F : A -> gen_spectrum N}
(f : Πa, E a →ₛ F a) : spi A E →ₛ spi A F := (f : Πa, E a →ₛ F a) : spi A E →ₛ spi A F :=