P1_of_eq — Mathlib

English

If x1 ≈ x3 and P2(x1,x3,y1) and P2(x1,x3,y3) and P3(x1,x2,y2,y3), then P1(x1,x2,x3,y1,y2,y3).

Русский

Если x1 ≈ x3 и P2(x1,x3,y1) и P2(x1,x3,y3) и P3(x1,x2,y2,y3), то P1(x1,x2,x3,y1,y2,y3).

LaTeX

$$$$ \text{If } x_1 \approx x_3 \text{ and } P2(x_1,x_3,y_1) \text{ and } P2(x_1,x_3,y_3) \text{ and } P3(x_1,x_2,y_2,y_3) \text{ then } P1(x_1,x_2,x_3,y_1,y_2,y_3). $$$$

Lean4

theorem P1_of_eq (he : x₁ ≈ x₃) (h₁ : P2 x₁ x₃ y₁) (h₃ : P2 x₁ x₃ y₃) (h3 : P3 x₁ x₂ y₂ y₃) : P1 x₁ x₂ x₃ y₁ y₂ y₃ :=
  by
  rw [P1, ← h₁ he, ← h₃ he, sub_lt_sub_iff]
  convert add_lt_add_left h3 ⟦x₁ * y₁⟧ using 1 <;> abel

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