feat(Propositional/Hilbert/F): prove DT_list, removing two sorries - #8
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`DT_list` (the deduction theorem for `List` contexts in the F-system) carried two `sorry`s since the Hilbert-systems redesign (FormalizedFormalLogic#812): the forward `ctx` case and the backward `hcons` case. They transitively block `DT_finset` / `DT_set`, which are proved via `DT_list`. `Entailment.F` provides neither `HasAxiomImplyK` nor `HasAxiomImplyS`, so the `Minimal`-layer `left_Conj₂!_intro` / `C_trans` are out of reach. This adds a private helper `F_conj₂_mem` that builds `⋀Γ 🡒 φ` from `φ ∈ Γ` using only F-level tools (`ruleI` transitivity + `and₁!`/`and₂!`), and fills both cases. `#print axioms DT_list` → `[propext, Classical.choice, Quot.sound]` (no `sorryAx`). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Promoted upstream → FormalizedFormalLogic#832. Closing this fork-internal staging PR. |
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What
Dispels the two
sorrys inDT_list(the deduction theorem forListcontexts in the F-system) inFoundation/Propositional/Hilbert/F/Deduction.lean.DT_listis now sorry-free.ctxcase →exact F_conj₂_mem (List.mem_toFinset.mp hφ)hconscase →Deduction.andIR(head viactx, tail viadeduct_conjlifted bydeduction_subset), discharged byDeduction.mpprivate lemma F_conj₂_mem : φ ∈ Γ → H ⊢ Γ.conj₂ 🡒 φ, built from F-level tools only (ruleItransitivity +and₁!/and₂!), becauseEntailment.Fprovides neitherHasAxiomImplyKnorHasAxiomImplyS(so theMinimal-layerleft_Conj₂!_intro/C_transare out of reach).Notes
master(post-change(FirstOrder): redesignFirstOrderFormalizedFormalLogic/Foundation#794 / Forward-port to Lean/mathlib v4.31.0 FormalizedFormalLogic/Foundation#830). Cherry-pick applied cleanly; no conflicts.+22 / -2, single file.lake build Foundation.Propositional.Hilbert.F.Deductiongreen.🤖 Generated with Claude Code