Theorem: trans_clos_monotone (Traat/chapter1.lean)

State before:
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
R' : A → A → Prop
⊢ (fun R R' => ∀ (x y : A), R x y → R' x y) R R' →
    (fun R R' => ∀ (x y : A), R x y → R' x y) (trans_clos R) (trans_clos R')
Tactic:
intros le x y tr
State after:
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
R' : A → A → Prop
le : ∀ (x y : A), R x y → R' x y
x y : A
tr : trans_clos R x y
⊢ trans_clos R' x y

State before:
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
R' : A → A → Prop
le : ∀ (x y : A), R x y → R' x y
x y : A
tr : trans_clos R x y
⊢ trans_clos R' x y
Tactic:
induction tr <;> aesop
State after:
no goals