Nuprl Lemma : mFOatomic_wf
∀[name:Atom]. ∀[vars:ℤ List].  (name(vars) ∈ mFOL())
Proof
Definitions occuring in Statement : 
mFOatomic: name(vars)
, 
mFOL: mFOL()
, 
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
, 
mFOL: mFOL()
, 
mFOatomic: name(vars)
, 
eq_atom: x =a y
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
subtype_rel: A ⊆r B
, 
ext-eq: A ≡ B
, 
and: P ∧ Q
, 
mFOLco_size: mFOLco_size(p)
, 
mFOL_size: mFOL_size(p)
, 
has-value: (a)↓
, 
nat: ℕ
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
Lemmas referenced : 
mFOLco-ext, 
list_wf, 
ifthenelse_wf, 
eq_atom_wf, 
mFOLco_wf, 
bool_wf, 
false_wf, 
le_wf, 
nat_wf, 
has-value_wf_base, 
set_subtype_base, 
int_subtype_base, 
is-exception_wf, 
equal_wf, 
has-value_wf-partial, 
set-value-type, 
int-value-type, 
mFOLco_size_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
dependent_set_memberEquality, 
introduction, 
extract_by_obid, 
hypothesis, 
sqequalRule, 
dependent_pairEquality, 
tokenEquality, 
hypothesisEquality, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
intEquality, 
instantiate, 
universeEquality, 
productEquality, 
atomEquality, 
voidEquality, 
applyEquality, 
productElimination, 
natural_numberEquality, 
independent_pairFormation, 
lambdaFormation, 
divergentSqle, 
sqleReflexivity, 
lambdaEquality, 
independent_isectElimination, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination
Latex:
\mforall{}[name:Atom].  \mforall{}[vars:\mBbbZ{}  List].    (name(vars)  \mmember{}  mFOL())
Date html generated:
2018_05_21-PM-10_20_53
Last ObjectModification:
2017_07_26-PM-06_37_39
Theory : minimal-first-order-logic
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