doc(examples/lean): cleanup
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
parent
fd8a1266d0
commit
7d6cd514d1
1 changed files with 7 additions and 4 deletions
|
@ -21,15 +21,18 @@ theorem tcls_refl {A : TypeU} (R : A → A → Bool) : ∀ a, R⁺ a a
|
|||
:= take a P, assume Hrefl Htrans Hsub,
|
||||
Hrefl a
|
||||
|
||||
theorem tcls_sub {A : TypeU} {R : A → A → Bool} {a b : A} (H : R a b) : R⁺ a b
|
||||
:= take P, assume Hrefl Htrans Hsub,
|
||||
Hsub a b H
|
||||
theorem tcls_sub {A : TypeU} (R : A → A → Bool) : R ⊆ R⁺
|
||||
:= take a b,
|
||||
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
|
||||
:= take P, assume 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 a b, assume H : R⁺ a b,
|
||||
have P a b : H P Hrefl Htrans Hsub
|
||||
|
|
Loading…
Reference in a new issue