support_inf — Mathlib

English

The infimum (coordinatewise) has support equal to the intersection of supports: (f ⊓ g).support = f.support ∩ g.support.

Русский

Первообразная слабого пересечения по координатам обладает опорой, равной пересечению опор: (f ⊓ g).support = f.support ∩ g.support.

LaTeX

$$$(f \wedge g).\mathrm{support} = f.\mathrm{support} \cap g.\mathrm{support}$$$

Lean4

@[simp]
theorem support_inf : (f ⊓ g).support = f.support ∩ g.support :=
  by
  ext
  simp only [inf_apply, mem_support_iff, Ne, Finset.mem_inter]
  simp only [← nonpos_iff_eq_zero, min_le_iff, not_or]

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