Nuprl Lemma : mFO-uniform-evidence_wf
∀[vs:ℤ List]. ∀[fmla:AbstractFOFormula(vs)]. (mFO-uniform-evidence(vs;fmla) ∈ 𝕌')
Proof
Definitions occuring in Statement :
mFO-uniform-evidence: mFO-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,
mFO-uniform-evidence: mFO-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)]. (mFO-uniform-evidence(vs;fmla) \mmember{} \mBbbU{}')
Date html generated:
2016_05_15-PM-10_12_19
Last ObjectModification:
2015_12_27-PM-06_33_50
Theory : minimal-first-order-logic
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