Nuprl Lemma : mFO_uniform_evidence_wf
∀[vs:ℤ List]. ∀[fmla:AbstractFOFormula(vs)]. (mFO_uniform_evidence{i:l}(fmla) ∈ 𝕌')
Proof
Definitions occuring in Statement :
mFO_uniform_evidence: mFO_uniform_evidence{i:l}(fmla),
AbstractFOFormula: AbstractFOFormula(vs),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFO_uniform_evidence: mFO_uniform_evidence{i:l}(fmla),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
FOAssignment: FOAssignment(vs,Dom),
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
istype: istype(T)
Lemmas referenced :
FOStruct_wf,
all_wf,
FOSatWith_wf,
subtype_rel_dep_function,
l_member_wf,
AbstractFOFormula_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
isectEquality,
closedConclusion,
universeEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
cumulativity,
functionEquality,
intEquality,
because_Cache,
lambdaEquality_alt,
applyEquality,
universeIsType,
setEquality,
lambdaFormation_alt,
setElimination,
rename,
setIsType,
independent_isectElimination,
functionIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[vs:\mBbbZ{} List]. \mforall{}[fmla:AbstractFOFormula(vs)]. (mFO\_uniform\_evidence\{i:l\}(fmla) \mmember{} \mBbbU{}')
Date html generated:
2019_10_16-AM-11_38_55
Last ObjectModification:
2018_10_14-PM-04_51_48
Theory : minimal-first-order-logic
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