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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