Theorem: Misc.Nat.add_eq_zero (LeanSAT/Util/Misc.lean)

State before:
a b : Nat
⊢ a + b = 0 ↔ a = 0 ∧ b = 0
Tactic:
constructor
State after:
case mp
a b : Nat
⊢ a + b = 0 → a = 0 ∧ b = 0

case mpr
a b : Nat
⊢ a = 0 ∧ b = 0 → a + b = 0

State before:
case mp
a b : Nat
⊢ a + b = 0 → a = 0 ∧ b = 0

case mpr
a b : Nat
⊢ a = 0 ∧ b = 0 → a + b = 0
Tactic:
. exact Nat.eq_zero_of_add_eq_zero
State after:
case mpr
a b : Nat
⊢ a = 0 ∧ b = 0 → a + b = 0

State before:
case mpr
a b : Nat
⊢ a = 0 ∧ b = 0 → a + b = 0
Tactic:
. intro h
  rw [h.1, h.2]
State after:
no goals

State before:
case mp
a b : Nat
⊢ a + b = 0 → a = 0 ∧ b = 0
Tactic:
exact Nat.eq_zero_of_add_eq_zero
State after:
no goals

State before:
case mpr
a b : Nat
⊢ a = 0 ∧ b = 0 → a + b = 0
Tactic:
intro h
State after:
case mpr
a b : Nat
h : a = 0 ∧ b = 0
⊢ a + b = 0

State before:
case mpr
a b : Nat
h : a = 0 ∧ b = 0
⊢ a + b = 0
Tactic:
rw [h.1, h.2]
State after:
no goals