foldl_ι — Mathlib

English

Let Q be a quadratic form on M. For a bilinear map f with the hf property, folding the generator ι_Q m under foldr' yields f m (1, n). In other words, foldr' Q f hf n (ι_Q m) = f m (1, n).

Русский

Пусть Q – квадратичная форма на M. Для f с hf, свёртка по генератору ι_Q m в foldr' даёт f m (1, n).

LaTeX

$$$\\foldr'_Q f hf n (\\iota_Q m) = f m (1, n)$$$

Lean4

@[simp]
theorem foldl_ι (f : M →ₗ[R] N →ₗ[R] N) (hf) (n : N) (m : M) : foldl Q f hf n (ι Q m) = f m n := by
  rw [← foldr_reverse, reverse_ι, foldr_ι]

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