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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