Nuprl Lemma : mobj-sq
∀[S:MutualRectypeSpec]. ∀[x:mobj(S)]. (x ~ <mobj-kind(x), mk-prec(mobj-label(x);mobj-tuple(x))>)
Proof
Definitions occuring in Statement :
mobj-tuple: mobj-tuple(x),
mobj-label: mobj-label(x),
mobj-kind: mobj-kind(x),
mobj: mobj(L),
mrec_spec: MutualRectypeSpec,
mk-prec: mk-prec(lbl;x),
uall: ∀[x:A]. B[x],
pair: <a, b>,
sqequal: s ~ t
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-tuple: mobj-tuple(x),
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-sq,
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,
axiomSqEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies
Latex:
\mforall{}[S:MutualRectypeSpec]. \mforall{}[x:mobj(S)]. (x \msim{} <mobj-kind(x), mk-prec(mobj-label(x);mobj-tuple(x))>)
Date html generated:
2019_06_20-PM-02_15_35
Last ObjectModification:
2019_02_28-PM-03_46_17
Theory : tuples
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