feat(Propositional/Hilbert/F): prove DT_list, removing two sorries#4
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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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v4.29.0 build check — the fork CI only triggers on
The eventual upstream PR (base = |
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Superseded by the rehomed version (post-FormalizedFormalLogic#794 master), now upstream as FormalizedFormalLogic#832. |
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What
Dispels the two
sorrys inDT_list(the deduction theorem forListcontexts in the F-system),Foundation/Propositional/Hilbert/F/Deduction.lean.DT_listis now sorry-free and axiom-clean.ctxcase →exact F_conj₂_mem (List.mem_toFinset.mp hφ)hconscase →Deduction.andIR(head viactx, tail viadeduct_conjlifted bydeduction_subset), discharged byDeduction.mpF_conj₂_mem : φ ∈ Γ → H ⊢ Γ.conj₂ 🡒 φ, built from F-level tools only (ruleItransitivity +and₁!/and₂!).Entailment.Fprovides neitherHasAxiomImplyKnorHasAxiomImplyS, so theMinimal-layerleft_Conj₂!_intro/C_transare out of reach.These holes have been present since the Hilbert-systems redesign (FormalizedFormalLogic#812) and transitively block
DT_finset/DT_set, which are proved viaDT_list.Verification
lean-sorryon the file → 0#print axioms DT_list→[propext, Classical.choice, Quot.sound](nosorryAx)master(Lean v4.29.0) — CI here is the v4.29.0 confirmation. The fix uses no version-specific tactics;ruleI/impIdand the rest all exist in v4.29.0.Why this PR lives in the fork
Canonical practice for external contributions: branched off the exact upstream-target SHA (
c28942b=FormalizedFormalLogic/Foundation@master) into basedt-list-dispel-base, so this PR's diff is identical to the eventual upstream diff and CI runs on the upstream toolchain. After approval here, it goes upstream as a PR againstFormalizedFormalLogic/Foundation:master.