Nuprl Lemma : mobj-label_wf
∀[S:MutualRectypeSpec]. ∀[x:mobj(S)]. (mobj-label(x) ∈ {lbl:Atom| 0 < ||mrec-spec(S;lbl;mobj-kind(x))||} )
Proof
Definitions occuring in Statement :
mobj-label: mobj-label(x),
mobj-kind: mobj-kind(x),
mobj: mobj(L),
mrec-spec: mrec-spec(L;lbl;p),
mrec_spec: MutualRectypeSpec,
length: ||as||,
less_than: a < b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
uimplies: b supposing a,
mobj: mobj(L),
mkinds: mKinds,
subtype_rel: A ⊆r B,
mobj-label: mobj-label(x),
mobj-kind: mobj-kind(x),
pi1: fst(t),
mobj-data: mobj-data(x),
pi2: snd(t),
mrec: mrec(L;i),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
mobj-ext,
ext-eq_inversion,
mobj_wf,
mrec_wf,
subtype_rel_weakening,
subtype_rel-equal,
mtype_wf,
mtype-sqequal,
prec-label_wf,
mrec-spec_wf,
mrec_spec_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
hypothesis_subsumption,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productEquality,
atomEquality,
independent_isectElimination,
because_Cache,
productElimination,
Error :dependent_pairEquality_alt,
setElimination,
rename,
applyEquality,
sqequalRule,
Error :universeIsType,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies
Latex:
\mforall{}[S:MutualRectypeSpec]. \mforall{}[x:mobj(S)].
(mobj-label(x) \mmember{} \{lbl:Atom| 0 < ||mrec-spec(S;lbl;mobj-kind(x))||\} )
Date html generated:
2019_06_20-PM-02_15_28
Last ObjectModification:
2019_02_28-PM-03_37_52
Theory : tuples
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