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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