From 1c51df13f2c47835789f76653fbf52fbb717b684 Mon Sep 17 00:00:00 2001 From: Egbert Rijke Date: Sat, 8 Jul 2017 14:49:32 +0100 Subject: [PATCH] further reductions to pointed_pi --- homotopy/spectrum.hlean | 19 +++++++++++++++++-- 1 file changed, 17 insertions(+), 2 deletions(-) diff --git a/homotopy/spectrum.hlean b/homotopy/spectrum.hlean index 17098b3..fa79d72 100644 --- a/homotopy/spectrum.hlean +++ b/homotopy/spectrum.hlean @@ -698,6 +698,20 @@ set_option pp.coercions true intro a, exact glue_square (f a) n, 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 {N : succ_str} {A : Type*} {E F : A → gen_spectrum N} (f : Π a, (E a) →ₛ (F a)) (n : N) : psquare @@ -707,8 +721,9 @@ set_option pp.coercions true (pequiv.to_pmap ppi_loop_pequiv⁻¹ᵉ*) := begin - exact sorry - end /- TODO FOR SSS -/ + refine (_)⁻¹ᵛ*, + fapply psquare_loop_ppi_compose_left, + end 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 :=