range_eval — Mathlib

English

For m ≤ n, the transition map composed with eval at n equals eval at m, i.e., transitionMap I M hmn ∘ eval I M n = eval I M m.

Русский

При m ≤ n композиция переходной карты и eval на n равна eval на m: transitionMap I M hmn ∘ eval I M n = eval I M m.

LaTeX

$$$ \\forall m,n \\in \\mathbb{N},\\; m \\le n \\Rightarrow (transitionMap I M hmn) \\circ (eval I M n) = eval I M m $$$

Lean4

@[simp]
theorem range_eval (n : ℕ) : LinearMap.range (eval I M n) = ⊤ :=
  LinearMap.range_eq_top.2 (eval_surjective I M n)

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