isPath_singleton — Mathlib

English

For a single input a, IsPath s t [a] is equivalent to t being reachable from s by a step a.

Русский

Для одного ввода a IsPath s t [a] эквивално достижимости t из s по шагу a.

LaTeX

$$M.IsPath s t [a] \\Leftrightarrow t \in M.step s a$$

Lean4

@[simp]
theorem isPath_singleton {a : Option α} : M.IsPath s t [a] ↔ t ∈ M.step s a
    where
  mp := by
    rintro (_ | ⟨_, _, _, _, _, _, ⟨⟩⟩)
    assumption
  mpr := by tauto

Похожие утверждения