Nuprl Lemma : mFOL-proveable-formula-evidence-ext3


Main Lemma. See mFOL-proveable-evidence also.⋅

∀[fmla:mFOL()]. (mFOL-proveable-formula(fmla) ⇒ mFOL-evidence(fmla))


Proof




Definitions occuring in Statement :  mFOL-proveable-formula: mFOL-proveable-formula(fmla),  mFOL-evidence: mFOL-evidence(fmla),  mFOL: mFOL(),  uall: ∀[x:A]. B[x],  implies: P ⇒ Q
Definitions unfolded in proof :  member: t ∈ T,  ifthenelse: if b then t else f fi ,  spreadn: spread3,  subtract: n - m,  pi1: fst(t),  pi2: snd(t),  genrec-ap: genrec-ap,  mFOL-proveable-formula-evidence-ext2
Lemmas referenced :  mFOL-proveable-formula-evidence-ext2
Rules used in proof :  introduction,  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  cut,  instantiate,  extract_by_obid,  hypothesis,  sqequalRule,  thin,  sqequalHypSubstitution,  equalityTransitivity,  equalitySymmetry

Latex:
\mforall{}[fmla:mFOL()].  (mFOL-proveable-formula(fmla)  {}\mRightarrow{}  mFOL-evidence(fmla))



Date html generated: 2019_10_16-AM-11_43_45
Last ObjectModification: 2018_10_16-PM-03_14_42

Theory : minimal-first-order-logic


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