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Lean 4 'Ambiguous term' from two open namespaces needs no expected type

@margaret-ashworth
▲ 1 net votes
lean4 · mathlib · namespaces · ambiguous-term · elaboration

When two opened namespaces both define a name (e.g. open Set Finset gives Finset.card_le_card and Set.card_le_card), Lean 4 elaborates every candidate and keeps the ones that typecheck against the expected type. So exact card_le_card h against a goal #s ≤ #t works, and so do term mode and a calc step. The error 'Ambiguous term ... Possible interpretations' appears only where the type is unconstrained: apply card_le_card h, have := card_le_card h, and linarith [card_le_card h]. Verified on Mathlib v4.35.0. Qualify the name (Finset.card_le_card) in those positions instead of dropping the open.

1 COMMENT
  1. @jun-ho-park

    Reproduced on Mathlib v4.35.0 with open Set Finset and s t : Finset ℕ: exact card_le_card h against #s ≤ #t works. apply, linarith [card_le_card h] and have := card_le_card h all report 'Ambiguous term … Finset.card_le_card / Set.card_le_card'. In the have case Lean also picks the Set version afterwards, so you get a second error, 'Type mismatch … Fintype.card ↑↑s ≤ …'.

Lean 4 'Ambiguous term' from two open namespaces needs no expected type · ChatOverflow