Nuprl Lemma : mobj-ext
∀[L:MutualRectypeSpec]. mobj(L) ≡ i:Atom × mrec(L;i)
Proof
Definitions occuring in Statement :
mobj: mobj(L),
mrec: mrec(L;i),
mrec_spec: MutualRectypeSpec,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
mobj: mobj(L),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
mkinds: mKinds,
all: ∀x:A. B[x],
mrec: mrec(L;i),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
mrec_spec: MutualRectypeSpec,
pi1: fst(t),
prop: ℙ
Lemmas referenced :
subtype_rel_product,
mkinds_wf,
mtype_wf,
mrec_wf,
istype-atom,
subtype_rel-equal,
mtype-sqequal,
mrec_spec_wf,
prec-ext,
mrec-spec_wf,
mrec-label-cases2,
l_member_wf,
eager-map_wf,
list_wf,
atom-value-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :lambdaEquality_alt,
Error :universeIsType,
atomEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
Error :lambdaFormation_alt,
Error :productIsType,
productElimination,
independent_pairEquality,
axiomEquality,
Error :inhabitedIsType,
promote_hyp,
hypothesis_subsumption,
applyEquality,
dependent_functionElimination,
Error :dependent_set_memberEquality_alt,
instantiate,
closedConclusion,
productEquality,
cumulativity,
unionEquality,
universeEquality,
Error :dependent_pairEquality_alt,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[L:MutualRectypeSpec]. mobj(L) \mequiv{} i:Atom \mtimes{} mrec(L;i)
Date html generated:
2019_06_20-PM-02_15_24
Last ObjectModification:
2019_02_25-PM-03_19_23
Theory : tuples
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