Nuprl Lemma : FO-uniform-evidence_wf
∀[vs:ℤ List]. ∀[fmla:AbstractFOFormula+(vs)].  (FO-uniform-evidence(vs;fmla) ∈ 𝕌')
Proof
Definitions occuring in Statement : 
FO-uniform-evidence: FO-uniform-evidence(vs;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
, 
FO-uniform-evidence: FO-uniform-evidence(vs;fmla)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
prop: ℙ
Lemmas referenced : 
FOStruct+_wf, 
all_wf, 
FOAssignment_wf, 
FOSatWith+_wf, 
AbstractFOFormula+_wf, 
list_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
isectEquality, 
universeEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
cumulativity, 
lambdaEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache, 
intEquality
Latex:
\mforall{}[vs:\mBbbZ{}  List].  \mforall{}[fmla:AbstractFOFormula+(vs)].    (FO-uniform-evidence(vs;fmla)  \mmember{}  \mBbbU{}')
Date html generated:
2016_05_15-PM-10_12_23
Last ObjectModification:
2015_12_27-PM-06_33_48
Theory : minimal-first-order-logic
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