disjoint_mk_iff — Mathlib

English

Disjoint of the representatives ⟨p, hp⟩ and ⟨q, hq⟩ in f.invtSubmodule is equivalent to Disjoint p q.

Русский

Пара подмодулей в представлении ⟨p, hp⟩ и ⟨q, hq⟩ дисjoint эквивалентно Disjoint p q.

LaTeX

$$$\text{Disjoint} (\langle p, hp\rangle) (\langle q, hq\rangle) \iff \text{Disjoint}(p, q)$$$

Lean4

@[simp]
protected theorem disjoint_mk_iff {p q : Submodule R M} (hp : p ∈ f.invtSubmodule) (hq : q ∈ f.invtSubmodule) :
    Disjoint (α := f.invtSubmodule) ⟨p, hp⟩ ⟨q, hq⟩ ↔ Disjoint p q := by
  rw [disjoint_iff, disjoint_iff, Sublattice.mk_inf_mk, Subtype.mk_eq_bot_iff (⊥ : f.invtSubmodule).property]

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