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

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

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

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

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

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

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

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

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