fstₗ_comp_inlₗ — Mathlib

English

In the lexicographic setting, the composition of fstₗ with inlₗ is the identity on α: fstₗ ∘ inlₗ = id on α.

Русский

В лексикографическом контексте композиция fstₗ с inlₗ равна тождеству на α: fstₗ ∘ inlₗ = id_α.

LaTeX

$$$$ fst_{Lex} \circ inl_{Lex} = \mathrm{id}_{\alpha}. $$$$

Lean4

@[to_additive (attr := simp)]
theorem fstₗ_comp_inlₗ : (fstₗ α β).comp (inlₗ α β) = .id α :=
  rfl

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