Nuprl Lemma : AbstractFOAtomic_wf
∀[n:Atom]. ∀[L:ℤ List]. (AbstractFOAtomic(n;L) ∈ AbstractFOFormula(L))
Proof
Definitions occuring in Statement :
AbstractFOAtomic: AbstractFOAtomic(n;L),
AbstractFOFormula: AbstractFOFormula(vs),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
AbstractFOFormula: AbstractFOFormula(vs),
AbstractFOAtomic: AbstractFOAtomic(n;L),
FOStruct: FOStruct(Dom),
prop: ℙ,
FOAssignment: FOAssignment(vs,Dom)
Lemmas referenced :
list-subtype,
map_wf,
l_member_wf,
FOAssignment_wf,
FOStruct_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
sqequalRule,
lambdaEquality,
applyEquality,
setEquality,
universeEquality,
axiomEquality,
isect_memberEquality,
because_Cache,
atomEquality
Latex:
\mforall{}[n:Atom]. \mforall{}[L:\mBbbZ{} List]. (AbstractFOAtomic(n;L) \mmember{} AbstractFOFormula(L))
Date html generated:
2016_05_15-PM-10_12_26
Last ObjectModification:
2015_12_27-PM-06_33_44
Theory : minimal-first-order-logic
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