Add missing hypotheses to mem_relint_dual and its sibling - #85
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Both relint duality lemmas were false as stated: * `mem_relint_iff_forall_dual_zero_le_mem_lineal_of_eq_zero` fails in infinite dimensions (for the lexicographic cone on `⊕ℕ R` the dual cone is trivial, making the right hand side vacuous while the relint is empty); it now assumes `C.FinRank`. Its forward direction holds unconditionally and is proven separately as `mem_lineal_dual_of_mem_relint`. * `mem_relint_dual` fails already in `R²` for non-dual-closed cones; it now assumes `C.DualClosed p` and `(dual p C).FinSalRank`. The `exists_dual_pos` example inherits the dual closedness assumption.
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Before #82 one could give much easier disproofs for these |
YaelDillies
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Sep 2, 2026
YaelDillies
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Sep 3, 2026
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Both relint duality lemmas were false as stated:
mem_relint_iff_forall_dual_zero_le_mem_lineal_of_eq_zerofails in infinite dimensions (for the lexicographic cone on⊕ℕ Rthe dual cone is trivial, making the right hand side vacuous while the relint is empty); it now assumesC.FinRank. Its forward direction holds unconditionally and is proven separately asmem_lineal_dual_of_mem_relint.mem_relint_dualfails already inR²for non-dual-closed cones; it now assumesC.DualClosed pand(dual p C).FinSalRank. Theexists_dual_posexample inherits the dual closedness assumption.