dirac_apply_eq_zero_or_one — Mathlib

English

A convenient simplification: dirac a s ≠ 0 is equivalent to dirac a s = 1.

Русский

Удобное упрощение: dirac a s ≠ 0 эквивалентно dirac a s = 1.

LaTeX

$$$$ dirac a s \neq 0 \iff dirac a s = 1 $$$$

Lean4

theorem dirac_apply_eq_zero_or_one : dirac a s = 0 ∨ dirac a s = 1 :=
  by
  rw [← measure_toMeasurable s, dirac_apply' a (measurableSet_toMeasurable ..), indicator]
  simp only [Pi.one_apply, ite_eq_right_iff, one_ne_zero, imp_false, ite_eq_left_iff, zero_ne_one, not_not]
  tauto

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