Theorem: Smt.Reconstruct.Arith.sumBounds₅ (Smt/Reconstruct/Arith/SumBounds/Lemmas.lean)

State before:
α : Type
inst✝ : LinearOrderedRing α
a b c d : α
⊢ a ≤ b → c ≤ d → a + c ≤ b + d
Tactic:
intros h₁ h₂
State after:
α : Type
inst✝ : LinearOrderedRing α
a b c d : α
h₁ : a ≤ b
h₂ : c ≤ d
⊢ a + c ≤ b + d

State before:
α : Type
inst✝ : LinearOrderedRing α
a b c d : α
h₁ : a ≤ b
h₂ : c ≤ d
⊢ a + c ≤ b + d
Tactic:
have r₁ : a + c ≤ a + d := add_le_add_left h₂ a
State after:
α : Type
inst✝ : LinearOrderedRing α
a b c d : α
h₁ : a ≤ b
h₂ : c ≤ d
r₁ : a + c ≤ a + d
⊢ a + c ≤ b + d

State before:
α : Type
inst✝ : LinearOrderedRing α
a b c d : α
h₁ : a ≤ b
h₂ : c ≤ d
r₁ : a + c ≤ a + d
⊢ a + c ≤ b + d
Tactic:
have r₂ : a + d ≤ b + d := add_le_add_right h₁ d
State after:
α : Type
inst✝ : LinearOrderedRing α
a b c d : α
h₁ : a ≤ b
h₂ : c ≤ d
r₁ : a + c ≤ a + d
r₂ : a + d ≤ b + d
⊢ a + c ≤ b + d

State before:
α : Type
inst✝ : LinearOrderedRing α
a b c d : α
h₁ : a ≤ b
h₂ : c ≤ d
r₁ : a + c ≤ a + d
r₂ : a + d ≤ b + d
⊢ a + c ≤ b + d
Tactic:
exact le_trans r₁ r₂
State after:
no goals