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doc(examples/lean): cleanup

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura 2014-01-16 05:01:34 -08:00
parent fd8a1266d0
commit 7d6cd514d1
1 changed files with 7 additions and 4 deletions
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11
examples/lean/tc.lean
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@ -21,15 +21,18 @@ theorem tcls_refl {A : TypeU} (R : A → A → Bool) : ∀ a, R⁺ a a
:= take a P, assume Hrefl Htrans Hsub, := take a P, assume Hrefl Htrans Hsub,
Hrefl a Hrefl a
theorem tcls_sub {A : TypeU} {R : A → A → Bool} {a b : A} (H : R a b) : R⁺ a b theorem tcls_sub {A : TypeU} (R : A → A → Bool) : R ⊆ R⁺
:= take P, assume Hrefl Htrans Hsub, := take a b,
Hsub a b H assume Hab : R a b,
have R⁺ a b :
take P, assume Hrefl Htrans Hsub,
Hsub a b Hab
theorem tcls_step {A : TypeU} {R : A → A → Bool} {a b c : A} (H1 : R a b) (H2 : R⁺ b c) : R⁺ a c theorem tcls_step {A : TypeU} {R : A → A → Bool} {a b c : A} (H1 : R a b) (H2 : R⁺ b c) : R⁺ a c
:= take P, assume Hrefl Htrans Hsub, := take P, assume Hrefl Htrans Hsub,
Htrans a b c (Hsub a b H1) (H2 P Hrefl Htrans Hsub) Htrans a b c (Hsub a b H1) (H2 P Hrefl Htrans Hsub)
theorem tcls_smallest {A : TypeU} {R : A → A → Bool} : ∀ P, (reflexive P) → (transitive P) → (R ⊆ P) → (R⁺ ⊆ P) theorem tcls_smallest {A : TypeU} (R : A → A → Bool) : ∀ P, (reflexive P) → (transitive P) → (R ⊆ P) → (R⁺ ⊆ P)
:= take P, assume Hrefl Htrans Hsub, := take P, assume Hrefl Htrans Hsub,
take a b, assume H : R⁺ a b, take a b, assume H : R⁺ a b,
have P a b : H P Hrefl Htrans Hsub have P a b : H P Hrefl Htrans Hsub