Step
*
of Lemma
mFOL-proveable-evidence
No Annotations
∀[s:mFOL-sequent()]. (mFOL-proveable(s)
⇒ mFOL-sequent-evidence(s))
BY
{ TACTIC:(Auto
THEN D -1
THEN Assert ⌜∀s:mFOL-sequent()
(correct_proof(mFOL-sequent();λsr.mFOLeffect(sr);s;pf)
⇒ mFOL-sequent-evidence(s))⌝⋅) }
1
.....assertion.....
1. [s] : mFOL-sequent()
2. pf : proof-tree(mFOL-sequent();FOLRule();λsr.mFOLeffect(sr))
3. [%2] : correct_proof(mFOL-sequent();λsr.mFOLeffect(sr);s;pf)
⊢ ∀s:mFOL-sequent(). (correct_proof(mFOL-sequent();λsr.mFOLeffect(sr);s;pf)
⇒ mFOL-sequent-evidence(s))
2
1. [s] : mFOL-sequent()
2. pf : proof-tree(mFOL-sequent();FOLRule();λsr.mFOLeffect(sr))
3. [%2] : correct_proof(mFOL-sequent();λsr.mFOLeffect(sr);s;pf)
4. ∀s:mFOL-sequent(). (correct_proof(mFOL-sequent();λsr.mFOLeffect(sr);s;pf)
⇒ mFOL-sequent-evidence(s))
⊢ mFOL-sequent-evidence(s)
Latex:
Latex:
No Annotations
\mforall{}[s:mFOL-sequent()]. (mFOL-proveable(s) {}\mRightarrow{} mFOL-sequent-evidence(s))
By
Latex:
TACTIC:(Auto
THEN D -1
THEN Assert \mkleeneopen{}\mforall{}s:mFOL-sequent()
(correct\_proof(mFOL-sequent();\mlambda{}sr.mFOLeffect(sr);s;pf)
{}\mRightarrow{} mFOL-sequent-evidence(s))\mkleeneclose{}\mcdot{})
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