Theorem: Lean4Axiomatic.Rational.le_substR_add (Lean4Axiomatic/Rational/Order.lean)

State before:
ℕ ℤ ℚ : Type
inst✝¹⁰ : Natural ℕ
inst✝⁹ : Integer ℤ
inst✝⁸ : Core ℚ
inst✝⁷ : Addition ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Negation ℚ
inst✝⁴ : Sign ℚ
inst✝³ : Subtraction ℚ
inst✝² : Reciprocation ℚ
inst✝¹ : Division ℚ
inst✝ : Order ℚ
p₁ p₂ q : ℚ
⊢ p₁ ≤ p₂ → q + p₁ ≤ q + p₂
Tactic:
intro (_ : p₁ ≤ p₂)
State after:
ℕ ℤ ℚ : Type
inst✝¹⁰ : Natural ℕ
inst✝⁹ : Integer ℤ
inst✝⁸ : Core ℚ
inst✝⁷ : Addition ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Negation ℚ
inst✝⁴ : Sign ℚ
inst✝³ : Subtraction ℚ
inst✝² : Reciprocation ℚ
inst✝¹ : Division ℚ
inst✝ : Order ℚ
p₁ p₂ q : ℚ
x✝ : p₁ ≤ p₂
⊢ q + p₁ ≤ q + p₂

State before:
ℕ ℤ ℚ : Type
inst✝¹⁰ : Natural ℕ
inst✝⁹ : Integer ℤ
inst✝⁸ : Core ℚ
inst✝⁷ : Addition ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Negation ℚ
inst✝⁴ : Sign ℚ
inst✝³ : Subtraction ℚ
inst✝² : Reciprocation ℚ
inst✝¹ : Division ℚ
inst✝ : Order ℚ
p₁ p₂ q : ℚ
x✝ : p₁ ≤ p₂
⊢ q + p₁ ≤ q + p₂
Tactic:
calc
  _ ≃ q + p₁ := eqv_refl
  _ ≃ p₁ + q := add_comm
  _ ≤ p₂ + q := le_substL_add ‹p₁ ≤ p₂›
  _ ≃ q + p₂ := add_comm
State after:
no goals