Nuprl Lemma : FOL-proveable-formula_wf
∀[fmla:mFOL()]. (FOL-proveable-formula(fmla) ∈ ℙ)
Proof
Definitions occuring in Statement :
FOL-proveable-formula: FOL-proveable-formula(fmla),
mFOL: mFOL(),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
FOL-proveable-formula: FOL-proveable-formula(fmla),
subtype_rel: A ⊆r B,
mFOL-sequent: mFOL-sequent(),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
FOL-proveable_wf,
nil_wf,
subtype_rel_product,
list_wf,
mFOL_wf,
subtype_rel_list,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
independent_pairEquality,
voidEquality,
hypothesis,
hypothesisEquality,
applyEquality,
lambdaEquality,
independent_isectElimination,
voidElimination,
lambdaFormation,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[fmla:mFOL()]. (FOL-proveable-formula(fmla) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-10_28_52
Last ObjectModification:
2015_12_27-PM-06_25_19
Theory : minimal-first-order-logic
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