mlieBracket_self — Mathlib

English

The swap of the arguments in the self bracket equals the negation of the swapped bracket, consistent with antisymmetry.

Русский

Перестановка аргументов в самоскобке сохраняет антисимметрию: [V,V] = 0 и [V,W] = -[W,V].

LaTeX

$$mlieBracket_swap_apply and mlieBracket_swap together imply antisymmetry: mlieBracket I V W = -mlieBracket I W V$$

Lean4

@[simp]
theorem mlieBracket_self : mlieBracket I V V = 0 := by ext x;
  simp_rw [mlieBracket, mlieBracketWithin_self, Pi.zero_apply]

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