Nuprl Lemma : varterm_wf
∀[opr:Type]. ∀[v:varname()]. varterm(v) ∈ term(opr) supposing ¬(v = nullvar() ∈ varname())
Proof
Definitions occuring in Statement :
varterm: varterm(v),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
varterm: varterm(v),
coterm-fun: coterm-fun(opr;T),
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
term-ext,
nullvar_wf,
istype-void,
list_wf,
varname_wf,
term_wf,
ext-eq_inversion,
coterm-fun_wf,
subtype_rel_weakening,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
inlEquality_alt,
dependent_set_memberEquality_alt,
sqequalRule,
functionIsType,
equalityIstype,
inhabitedIsType,
productIsType,
universeIsType,
productEquality,
applyEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[v:varname()]. varterm(v) \mmember{} term(opr) supposing \mneg{}(v = nullvar())
Date html generated:
2020_05_19-PM-09_53_39
Last ObjectModification:
2020_03_09-PM-04_08_16
Theory : terms
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