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+{i:l}(Dom),
FOStruct: FOStruct(Dom),
prop: ℙ,
FOAssignment: FOAssignment(vs,Dom),
subtype_rel: A ⊆r B
Lemmas referenced :
list-subtype,
b-union_wf,
map_wf,
l_member_wf,
nil_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,
setElimination,
rename,
setEquality,
universeEquality,
tokenEquality,
because_Cache,
axiomEquality,
isect_memberEquality,
atomEquality
Latex:
\mforall{}[n:Atom]. \mforall{}[L:\mBbbZ{} List]. (AbstractFOAtomic+(n;L) \mmember{} AbstractFOFormula+(L))
Date html generated:
2016_05_15-PM-10_12_28
Last ObjectModification:
2015_12_27-PM-06_33_43
Theory : minimal-first-order-logic
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