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Without the maps-to condition the conclusion only asserts an injection from Dyck (n-1)-paths into the paths with no even return, not a one-to-one correspondence. See trishullab#363.
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Fixes the Lean part of #363.
The conclusion only required every Dyck (n−1)-path to have a unique preimage among the Dyck n-paths with no even return, so for n ≥ 2 it was equivalent to |dyckpath (n - 1)| ≤ |dyckpath n ∩ noevenreturn n| rather than a one-to-one correspondence. This adds the maps-to condition:
(∀ x ∈ dyckpath n ∩ noevenreturn n, f x ∈ dyckpath (n - 1)) ∧One-line change. The statement elaborates (checked with
import Mathlibon live.lean-lang.org, Lean v4.35.0-rc4; only the expectedsorrywarning). The Isabelle issues described in #363 are left for a separate change, since they also need thep i→p kfix (#323) and the{..<2*m}range fix.