Theorem: Lean4Axiomatic.Rational.order_from_min_max (Lean4Axiomatic/Rational/Metric.lean)

State before:
ℕ ℤ ℚ : Type
inst✝¹² : Natural ℕ
inst✝¹¹ : Integer ℤ
inst✝¹⁰ : Core ℚ
inst✝⁹ : Addition ℚ
inst✝⁸ : Negation ℚ
inst✝⁷ : Subtraction ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Reciprocation ℚ
inst✝⁴ : Division ℚ
inst✝³ : Sign ℚ
inst✝² : Order ℚ
inst✝¹ : MinMax ℚ
inst✝ : Metric ℚ
p q r : ℚ
⊢ Ordered.min p q ≤ r ∧ r ≤ Ordered.max p q → p ≤ q → p ≤ r ∧ r ≤ q
Tactic:
intro (_ : min p q ≤ r ∧ r ≤ max p q) (_ : p ≤ q)
State after:
ℕ ℤ ℚ : Type
inst✝¹² : Natural ℕ
inst✝¹¹ : Integer ℤ
inst✝¹⁰ : Core ℚ
inst✝⁹ : Addition ℚ
inst✝⁸ : Negation ℚ
inst✝⁷ : Subtraction ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Reciprocation ℚ
inst✝⁴ : Division ℚ
inst✝³ : Sign ℚ
inst✝² : Order ℚ
inst✝¹ : MinMax ℚ
inst✝ : Metric ℚ
p q r : ℚ
x✝¹ : Ordered.min p q ≤ r ∧ r ≤ Ordered.max p q
x✝ : p ≤ q
⊢ p ≤ r ∧ r ≤ q

State before:
ℕ ℤ ℚ : Type
inst✝¹² : Natural ℕ
inst✝¹¹ : Integer ℤ
inst✝¹⁰ : Core ℚ
inst✝⁹ : Addition ℚ
inst✝⁸ : Negation ℚ
inst✝⁷ : Subtraction ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Reciprocation ℚ
inst✝⁴ : Division ℚ
inst✝³ : Sign ℚ
inst✝² : Order ℚ
inst✝¹ : MinMax ℚ
inst✝ : Metric ℚ
p q r : ℚ
x✝¹ : Ordered.min p q ≤ r ∧ r ≤ Ordered.max p q
x✝ : p ≤ q
⊢ p ≤ r ∧ r ≤ q
Tactic:
exact (order_iff_min_max ‹p ≤ q›).mpr ‹min p q ≤ r ∧ r ≤ max p q›
State after:
no goals