mathlib documentation

tactic.omega.misc

theorem omega.fun_mono_2 {α β γ : Type} {p : α → β → γ} {a1 a2 : α} {b1 b2 : β} :
a1 = a2b1 = b2p a1 b1 = p a2 b2

theorem omega.pred_mono_2 {α β : Type} {p : α → β → Prop} {a1 a2 : α} {b1 b2 : β} :
a1 = a2b1 = b2(p a1 b1 p a2 b2)

theorem omega.pred_mono_2' {c : Prop → Prop → Prop} {a1 a2 b1 b2 : Prop} :
(a1 a2)(b1 b2)(c a1 b1 c a2 b2)

def omega.update {α : Type} :
α → ( → α) → α

Update variable assignment for a specific variable and leave everything else unchanged

Equations
theorem omega.update_eq {α : Type} (m : ) (a : α) (v : → α) :
v m a m = a

theorem omega.update_eq_of_ne {α : Type} {m : } {a : α} {v : → α} (k : ) :
k mv m a k = v k

def omega.update_zero {α : Type} :
α → ( → α) → α

Assign a new value to the zeroth variable, and push all other assignments up by 1

Equations

Intro with a fresh name

meta def omega.revert_cond  :
(exprtactic unit)exprtactic unit

Revert an expr if it passes the given test

meta def omega.revert_cond_all  :

Revert all exprs in the context that pass the given test

meta def omega.app_first {α β : Type} :
(α → tactic β)list αtactic β

Try applying a tactic to each of the element in a list until success, and return the first successful result