Nuprl Lemma : assert-not-isvarterm
∀[opr:Type]. ∀t:term(opr). (¬↑isvarterm(t) 
⇐⇒ ∃f:opr. ∃bts:bound-term(opr) List. (t = mkterm(f;bts) ∈ term(opr)))
Proof
Definitions occuring in Statement : 
bound-term: bound-term(opr)
, 
mkterm: mkterm(opr;bts)
, 
isvarterm: isvarterm(t)
, 
term: term(opr)
, 
list: T List
, 
assert: ↑b
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
not: ¬A
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
false: False
, 
rev_implies: P 
⇐ Q
, 
exists: ∃x:A. B[x]
, 
bound-term: bound-term(opr)
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
uimplies: b supposing a
, 
coterm-fun: coterm-fun(opr;T)
, 
isvarterm: isvarterm(t)
, 
isl: isl(x)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
true: True
, 
bfalse: ff
, 
mkterm: mkterm(opr;bts)
, 
squash: ↓T
, 
prop: ℙ
Lemmas referenced : 
term-ext, 
istype-assert, 
isvarterm_wf, 
istype-void, 
list_wf, 
bound-term_wf, 
mkterm_wf, 
term_wf, 
istype-universe, 
subtype_rel_weakening, 
coterm-fun_wf, 
istype-true, 
iff_weakening_uiff, 
assert_wf, 
assert_functionality_wrt_uiff, 
squash_wf, 
true_wf
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaFormation_alt, 
independent_pairFormation, 
sqequalRule, 
functionIsType, 
productElimination, 
independent_functionElimination, 
voidElimination, 
because_Cache, 
productIsType, 
universeIsType, 
equalityIstype, 
inhabitedIsType, 
instantiate, 
universeEquality, 
applyEquality, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
unionElimination, 
natural_numberEquality, 
dependent_pairFormation_alt, 
lambdaEquality_alt, 
imageElimination, 
imageMemberEquality, 
baseClosed
Latex:
\mforall{}[opr:Type]
    \mforall{}t:term(opr).  (\mneg{}\muparrow{}isvarterm(t)  \mLeftarrow{}{}\mRightarrow{}  \mexists{}f:opr.  \mexists{}bts:bound-term(opr)  List.  (t  =  mkterm(f;bts)))
Date html generated:
2020_05_19-PM-09_53_51
Last ObjectModification:
2020_03_09-PM-04_08_23
Theory : terms
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