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fix(init.path): a couple of small simplifications

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Floris van Doorn 2015-08-04 21:02:33 +02:00 committed by Leonardo de Moura
parent 0ec525a8ee
commit f3ba81a19d
1 changed files with 6 additions and 6 deletions
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12
hott/init/path.hlean
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@ -573,19 +573,19 @@ namespace eq
-- Whiskering and identity paths.
definition whisker_right_idp_right {p q : x = y} (h : p = q) :
definition whisker_right_idp {p q : x = y} (h : p = q) :
whisker_right h idp = h :=
eq.rec_on h (eq.rec_on p idp)
definition whisker_right_idp_left (p : x = y) (q : y = z) :
whisker_right idp q = idp :> (p ⬝ q = p ⬝ q) :=
eq.rec_on q idp
idp
definition whisker_left_idp_right (p : x = y) (q : y = z) :
whisker_left p idp = idp :> (p ⬝ q = p ⬝ q) :=
eq.rec_on q idp
idp
definition whisker_left_idp_left {p q : x = y} (h : p = q) :
definition whisker_left_idp {p q : x = y} (h : p = q) :
(idp_con p) ⁻¹ ⬝ whisker_left idp h ⬝ idp_con q = h :=
eq.rec_on h (eq.rec_on p idp)
@ -624,11 +624,11 @@ namespace eq
eq.rec_on q (eq.rec_on p idp)
definition eckmann_hilton {x:A} (p q : idp = idp :> x = x) : p ⬝ q = q ⬝ p :=
(!whisker_right_idp_right ◾ !whisker_left_idp_left)⁻¹
(!whisker_right_idp ◾ !whisker_left_idp)⁻¹
⬝ whisker_left _ !idp_con
⬝ !whisker_right_con_whisker_left
⬝ whisker_right !idp_con⁻¹ _
⬝ (!whisker_left_idp_left ◾ !whisker_right_idp_right)
⬝ (!whisker_left_idp ◾ !whisker_right_idp)
-- The action of functions on 2-dimensional paths
definition ap02 [unfold 8] [reducible] (f : A → B) {x y : A} {p q : x = y} (r : p = q)