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fix(13): change finset.induction to Lean text
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spl authored and soonhokong committed Feb 5, 2016
1 parent 6187d60 commit 7b2f5a1
Showing 1 changed file with 10 additions and 5 deletions.
15 changes: 10 additions & 5 deletions 13_More_Tactics.org
Original file line number Diff line number Diff line change
Expand Up @@ -74,12 +74,17 @@ property =P= holds for an arbitrary finite set when it holds for the
empty set and when it is maintained for a finite set =s= after a new
element =a=, that was not previosly in =s=, is added to =s=. This is
encapsulated by the following principle of induction:
# TODO: this should be Lean text
#+BEGIN_SRC text
#+BEGIN_SRC lean
open finset
namespace hide
-- BEGIN
theorem finset.induction {A : Type} [h : decidable_eq A] {P : finset A → Prop}
(H1 : P empty)
(H2 : ∀ ⦃a : A⦄, ∀{s : finset A}, a ∉ s → P s → P (insert a s)) :
∀s, P s
(H₁ : P finset.empty)
(H₂ : ∀ ⦃a : A⦄ {s : finset A}, a ∉ s → P s → P (insert a s))
: (∀ s, P s)
-- END
:= sorry
end hide
#+END_SRC
To use this as an induction principle, one has to mark it with the
attribute =[recursor 6]=, which tells the induction tactic that this
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