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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