Nuprl Lemma : mrec-spec_wf
∀[L:MutualRectypeSpec]. ∀[lbl,p:Atom]. (mrec-spec(L;lbl;p) ∈ (Atom + Atom + Type) List)
Proof
Definitions occuring in Statement :
mrec-spec: mrec-spec(L;lbl;p),
mrec_spec: MutualRectypeSpec,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
atom: Atom,
universe: Type
Definitions unfolded in proof :
mrec_spec: MutualRectypeSpec,
uall: ∀[x:A]. B[x],
member: t ∈ T,
mrec-spec: mrec-spec(L;lbl;p),
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
apply-alist_wf,
atom-deq_wf,
list_wf,
nil_wf,
istype-atom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
atomEquality,
hypothesis,
hypothesisEquality,
productEquality,
unionEquality,
universeEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :universeIsType
Latex:
\mforall{}[L:MutualRectypeSpec]. \mforall{}[lbl,p:Atom]. (mrec-spec(L;lbl;p) \mmember{} (Atom + Atom + Type) List)
Date html generated:
2019_06_20-PM-02_14_40
Last ObjectModification:
2019_02_24-PM-01_00_59
Theory : tuples
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