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Step * 1 13 1 of Lemma FOL-proveable-evidence


1. hyps : mFOL() List
2. concl : mFOL()
3. subgoals : mFOL-sequent() List
4. subproofs : ℕ||subgoals|| ⟶ proof-tree(mFOL-sequent();FOLRule();λsr.FOLeffect(sr))
5. ∀b:ℕ||subgoals||. ∀s:mFOL-sequent().
     (correct_proof(mFOL-sequent();λsr.FOLeffect(sr);s;subproofs b) ⇒ FOL-sequent-evidence{i:l}(s))
6. ∀i:ℕ||subgoals||. correct_proof(mFOL-sequent();λsr.FOLeffect(sr);subgoals[i];subproofs i)
7. hypnum : ℕ
8. hypnum < ||hyps||
9. [] = subgoals ∈ (mFOL-sequent() List)
10. ↑mFOatomic?(hyps[hypnum])
11. mFOatomic-name(hyps[hypnum]) = "false" ∈ Atom
12. mFOatomic-vars(hyps[hypnum]) = [] ∈ (ℤ List)
⊢ FOL-sequent-evidence{i:l}(<hyps, concl>)
BY
{ (Using [`i',⌜hypnum⌝] (BLemma `FOL-sequent-evidence-false-hyp`)⋅ THEN Auto) }

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Latex:

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Latex:

1.  hyps  :  mFOL()  List
2.  concl  :  mFOL()
3.  subgoals  :  mFOL-sequent()  List
4.  subproofs  :  \mBbbN{}||subgoals||  {}\mrightarrow{}  proof-tree(mFOL-sequent();FOLRule();\mlambda{}sr.FOLeffect(sr))
5.  \mforall{}b:\mBbbN{}||subgoals||.  \mforall{}s:mFOL-sequent().
          (correct\_proof(mFOL-sequent();\mlambda{}sr.FOLeffect(sr);s;subproofs  b)  {}\mRightarrow{}  FOL-sequent-evidence\{i:l\}(s))
6.  \mforall{}i:\mBbbN{}||subgoals||.  correct\_proof(mFOL-sequent();\mlambda{}sr.FOLeffect(sr);subgoals[i];subproofs  i)
7.  hypnum  :  \mBbbN{}
8.  hypnum  <  ||hyps||
9.  []  =  subgoals
10.  \muparrow{}mFOatomic?(hyps[hypnum])
11.  mFOatomic-name(hyps[hypnum])  =  "false"
12.  mFOatomic-vars(hyps[hypnum])  =  []
\mvdash{}  FOL-sequent-evidence\{i:l\}(<hyps,  concl>)


By

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Latex:
(Using  [`i',\mkleeneopen{}hypnum\mkleeneclose{}]  (BLemma  `FOL-sequent-evidence-false-hyp`)\mcdot{}  THEN  Auto)

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