Theorem: Smt.Reconstruct.Arith.sumBounds₄ (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_lt_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 lt_of_lt_of_le r₁ r₂
State after:
no goals