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fix(12): rename encB to encA
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To reflect the binding to `encodable A`.
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spl authored and soonhokong committed Feb 4, 2016
1 parent 0d17ef3 commit 848976e
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions 12_Axioms.org
Original file line number Diff line number Diff line change
Expand Up @@ -1185,9 +1185,9 @@ section
parameter (f : A → B)
parameter [inhA : inhabited A]
parameter [dex : ∀ b, decidable (∃ a, f a = b)]
parameter [encB : encodable A]
parameter [encA : encodable A]
parameter [deqB : decidable_eq B]
include inhA dex encB deqB
include inhA dex encA deqB

definition finv : B → A :=
λ b : B, if ex : (∃ a, f a = b) then choose ex else arbitrary A
Expand All @@ -1205,7 +1205,7 @@ end
#+END_SRC
The argument is essentially the same as the classical one; we have
simply replaced the classical =some= with the constructive choice
function =choose=, and added three extra hypotheses: =dex=, =encB= and
function =choose=, and added three extra hypotheses: =dex=, =encA= and
=deqB=. The first one makes sure we can decide whether a value =b= is
in the image of =f= or not, and the last two are needed to use
=choose=.
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