le_card_nonuniformWitness — Mathlib

English

If not ε-uniform, then #S · ε ≤ |W1| and #T · ε ≤ |W2|, where W1,W2 are the witnesses.

Русский

Если не существует ε-однородности, то мощности свидетелей удовлетворяют: |S|·ε ≤ |W1| и |T|·ε ≤ |W2|.

LaTeX

$$#s * ε ≤ #(G.nonuniformWitness ε s t).fst.card$$

Lean4

theorem le_card_nonuniformWitness (h : ¬G.IsUniform ε s t) : #s * ε ≤ #(G.nonuniformWitness ε s t) :=
  by
  unfold nonuniformWitness
  split_ifs
  · exact G.left_nonuniformWitnesses_card h
  · exact G.right_nonuniformWitnesses_card fun i => h i.symm

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