Nuprl Lemma : mk-prec_wf-mrec
∀[L:MutualRectypeSpec]. ∀[i,labl:Atom]. ∀[x:tuple-type(prec-arg-types(lbl,p.mrec-spec(L;lbl;p);i;labl))].
mk-prec(labl;x) ∈ mrec(L;i) supposing 0 < ||mrec-spec(L;labl;i)||
Proof
Definitions occuring in Statement :
mrec: mrec(L;i),
mrec-spec: mrec-spec(L;lbl;p),
mrec_spec: MutualRectypeSpec,
mk-prec: mk-prec(lbl;x),
prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl),
tuple-type: tuple-type(L),
length: ||as||,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
mrec: mrec(L;i)
Lemmas referenced :
mk-prec_wf,
mrec-spec_wf,
istype-less_than,
length_wf,
subtype_rel_self,
mrec_wf,
tuple-type_wf,
prec-arg-types_wf,
istype-atom,
mrec_spec_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
atomEquality,
sqequalRule,
Error :lambdaEquality_alt,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
instantiate,
unionEquality,
cumulativity,
universeEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :universeIsType
Latex:
\mforall{}[L:MutualRectypeSpec]. \mforall{}[i,labl:Atom].
\mforall{}[x:tuple-type(prec-arg-types(lbl,p.mrec-spec(L;lbl;p);i;labl))].
mk-prec(labl;x) \mmember{} mrec(L;i) supposing 0 < ||mrec-spec(L;labl;i)||
Date html generated:
2019_06_20-PM-02_16_30
Last ObjectModification:
2019_02_25-AM-00_17_46
Theory : tuples
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