Nuprl Lemma : assert-isvarterm
∀[opr:Type]
  ∀t:term(opr). (↑isvarterm(t) 
⇐⇒ ∃v:{v:varname()| ¬(v = nullvar() ∈ varname())} . (t = varterm(v) ∈ term(opr)))
Proof
Definitions occuring in Statement : 
varterm: varterm(v)
, 
isvarterm: isvarterm(t)
, 
term: term(opr)
, 
nullvar: nullvar()
, 
varname: varname()
, 
assert: ↑b
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
not: ¬A
, 
set: {x:A| B[x]} 
, 
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
, 
rev_implies: P 
⇐ Q
, 
exists: ∃x:A. B[x]
, 
not: ¬A
, 
false: False
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
coterm-fun: coterm-fun(opr;T)
, 
isvarterm: isvarterm(t)
, 
isl: isl(x)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
varterm: varterm(v)
, 
prop: ℙ
, 
bfalse: ff
, 
squash: ↓T
, 
true: True
, 
uiff: uiff(P;Q)
, 
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced : 
term-ext, 
istype-assert, 
isvarterm_wf, 
assert_witness, 
varname_wf, 
nullvar_wf, 
istype-void, 
varterm_wf, 
term_wf, 
istype-universe, 
subtype_rel_weakening, 
coterm-fun_wf, 
subtype_rel_union, 
not_wf, 
equal_wf, 
list_wf, 
ext-eq_inversion, 
subtype_rel_transitivity, 
istype-true, 
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, 
productElimination, 
because_Cache, 
independent_functionElimination, 
sqequalRule, 
productIsType, 
setIsType, 
universeIsType, 
functionIsType, 
equalityIstype, 
inhabitedIsType, 
setElimination, 
rename, 
independent_isectElimination, 
voidElimination, 
instantiate, 
universeEquality, 
applyEquality, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
unionElimination, 
dependent_pairFormation_alt, 
setEquality, 
voidEquality, 
productEquality, 
lambdaEquality_alt, 
unionEquality, 
inlEquality_alt, 
imageElimination, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed
Latex:
\mforall{}[opr:Type].  \mforall{}t:term(opr).  (\muparrow{}isvarterm(t)  \mLeftarrow{}{}\mRightarrow{}  \mexists{}v:\{v:varname()|  \mneg{}(v  =  nullvar())\}  .  (t  =  varterm(v)))
Date html generated:
2020_05_19-PM-09_53_44
Last ObjectModification:
2020_03_09-PM-04_08_18
Theory : terms
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