Nuprl Lemma : not-isvarterm-implies
∀[opr:Type]. ∀t:term(opr). ((¬↑isvarterm(t)) ⇒ (t = mkterm(term-opr(t);term-bts(t)) ∈ term(opr)))
Proof
Definitions occuring in Statement :
term-bts: term-bts(t),
term-opr: term-opr(t),
mkterm: mkterm(opr;bts),
isvarterm: isvarterm(t),
term: term(opr),
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
not: ¬A,
false: False,
true: True,
squash: ↓T,
term-opr: term-opr(t),
pi1: fst(t),
outr: outr(x),
mkterm: mkterm(opr;bts),
term-bts: term-bts(t),
pi2: snd(t),
bound-term: bound-term(opr),
prop: ℙ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
rev_implies: P ⇐ Q
Lemmas referenced :
assert-not-isvarterm,
istype-assert,
isvarterm_wf,
istype-void,
term_wf,
istype-universe,
mkterm_wf,
equal_wf,
squash_wf,
true_wf,
list_wf,
varname_wf,
term-opr_wf,
not_wf,
assert_wf,
term-bts_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
sqequalRule,
functionIsType,
universeIsType,
lambdaEquality_alt,
axiomEquality,
functionIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality,
because_Cache,
natural_numberEquality,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
productEquality,
independent_isectElimination
Latex:
\mforall{}[opr:Type]. \mforall{}t:term(opr). ((\mneg{}\muparrow{}isvarterm(t)) {}\mRightarrow{} (t = mkterm(term-opr(t);term-bts(t))))
Date html generated:
2020_05_19-PM-09_53_57
Last ObjectModification:
2020_03_11-PM-03_48_30
Theory : terms
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