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Box and cap tactics #467

Merged
merged 5 commits into from
Nov 21, 2018
Merged

Box and cap tactics #467

merged 5 commits into from
Nov 21, 2018

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favonia
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@favonia favonia commented Nov 20, 2018

Close #410, mostly.

@favonia favonia requested review from jonsterling and removed request for jonsterling November 20, 2018 15:07
@favonia favonia changed the title Box and cap tactics [WIP] Box and cap tactics Nov 20, 2018
@favonia favonia requested a review from jonsterling November 20, 2018 20:29
@favonia favonia self-assigned this Nov 20, 2018
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favonia commented Nov 21, 2018

BTW, this works in this PR:

def lemma0
  (A : [i] type [])
  (B : [i] type [i=0 → A 0])
  (C : [i] type [i=0 → A 1])
  : type
  = [i] (comp 0 1 (A i) [i=0 → B | i=1 → C]) []

def lemma1
  (A : [i] type [])
  (B : [i] type [i=0 → A 0])
  (C : [i] type [i=0 → A 1])
  (b : B 1)
  (c : C 1)
  (a : [i] A i [i = 0 → coe 1 0 b in B | i = 1 → coe 1 0 c in C])
  : lemma0 A B C
  = λ i → box (a i) [b | c]

def lemma2
  (A : [i] type [])
  (B : [i] type [i=0 → A 0])
  (C : [i] type [i=0 → A 1])
  (b : B 1)
  (c : C 1)
  (a : [i] A i [i = 0 → coe 1 0 b in B | i = 1 → coe 1 0 c in C])
  : [i] A i []
  = λ i → lemma1 A B C b c a i .cap

let cap (k m : 𝕀) = st (p k) (q k) (λ c → c (square k)) m in
comp 0 1 (cap j i) [
let mycap (k m : 𝕀) = st (p k) (q k) (λ c → c (square k)) m in
comp 0 1 (mycap j i) [
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@ecavallo please feel free to hijack this PR and put in some reasonable names.

@favonia favonia merged commit c95d1a0 into master Nov 21, 2018
@favonia favonia deleted the box-tactic branch November 21, 2018 00:21
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2 participants