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Five small formal corrections noticed during the Turkish translation #433

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@KokunoYumeto

While preparing the complete Turkish edition against Open Logic commit 9620cc7, we noticed five localized issues in the English source. Each was independently replayed against that exact tree; these are source notes only, not a request to review or merge the translation.

  1. functions/inverses.tex, lines 62–84: an injective f:A→B need not have a left inverse when A=∅ and B≠∅; the proof also chooses a∈A. Small fix: assume A≠∅ (or treat the empty case separately).
  2. rules-G3i.tex, lines 41–43: right-∨ uses the multi-succedent premise Γ ⊢ A,B, contrary to G3i's single-succedent restriction. Small fix: use Γ ⊢ A_i / Γ ⊢ A_1∨A_2 for i=1,2.
  3. proof-search/tableaux.tex, lines 25–29: the initial tableau for A,B ⊢ C,D signs D true, although both succedent formulas must be false. Small fix: change T D to F D.
  4. propositions-as-types/types.tex, lines 42–52: the case clause binds x,y but uses x_1,x_2; additionally, untypable proof terms exist, so “has exactly one type” should be “has at most one type” (or “if it has a type, that type is unique”).
  5. interpretation-rules.tex, lines 49–52: the second XOR rule concludes with A⊕B in the antecedent, so its label should be left-⊕, not right-⊕.

The Turkish release and compact provenance bundle contain the corresponding transparent dispositions. Work performed at Floris's direction by OpenAI 5.6 Sol, Ultra mode (OpenAI's current flagship model for complex work).

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