card_base_support_eq_two — Mathlib

English

Cardinality statement of item 133811 consistent with item 133809.

Русский

Соответствие кардинальности пункта 133811 кардинальности пункта 133809.

LaTeX

$$Nat.card ι = 12$$

Lean4

@[simp]
theorem card_base_support_eq_two : b.support.card = 2 :=
  by
  have _i : P.EmbeddedG2 := toEmbeddedG2 P
  have _i : Nonempty ι := IsG2.nonempty P
  rw [← Fintype.card_fin 2, ← Module.finrank_eq_card_basis (EmbeddedG2.basis P),
    Module.finrank_eq_card_basis (b.toWeightBasis (P := P.toRootSystem)), Fintype.card_coe]

Похожие утверждения