Theorem: LawfulLT.lt_of_eq_or_lt_of_lt (Algdata/Init/LawfulLT.lean)

State before:
α : Type u_1
inst✝ : LawfulLT α
a b c : α
⊢ a = b ∨ a < b → b < c → a < c
Tactic:
intro hab hbc
State after:
α : Type u_1
inst✝ : LawfulLT α
a b c : α
hab : a = b ∨ a < b
hbc : b < c
⊢ a < c

State before:
α : Type u_1
inst✝ : LawfulLT α
a b c : α
hab : a = b ∨ a < b
hbc : b < c
⊢ a < c
Tactic:
cases hab
State after:
case inl
α : Type u_1
inst✝ : LawfulLT α
a b c : α
hbc : b < c
h✝ : a = b
⊢ a < c

case inr
α : Type u_1
inst✝ : LawfulLT α
a b c : α
hbc : b < c
h✝ : a < b
⊢ a < c

State before:
α : Type u_1
inst✝ : LawfulLT α
a b c : α
hbc : b < c
h : a = b
⊢ a < c
Tactic:
case inl h => cases h; exact hbc
State after:
no goals

State before:
α : Type u_1
inst✝ : LawfulLT α
a b c : α
hbc : b < c
h : a < b
⊢ a < c
Tactic:
case inr h => exact trans h hbc
State after:
no goals

State before:
α : Type u_1
inst✝ : LawfulLT α
a b c : α
hbc : b < c
h : a = b
⊢ a < c
Tactic:
cases h
State after:
case refl
α : Type u_1
inst✝ : LawfulLT α
a c : α
hbc : a < c
⊢ a < c

State before:
case refl
α : Type u_1
inst✝ : LawfulLT α
a c : α
hbc : a < c
⊢ a < c
Tactic:
exact hbc
State after:
no goals

State before:
α : Type u_1
inst✝ : LawfulLT α
a b c : α
hbc : b < c
h : a < b
⊢ a < c
Tactic:
exact trans h hbc
State after:
no goals