Nuprl Lemma : mobj-cases
∀[S:MutualRectypeSpec]. ∀[P:mobj(S) ⟶ TYPE].
((∀k:mKinds. ∀lbl:{lbl:Atom| 0 < ||mrec-spec(S;lbl;k)||} .
∀t:tuple-type(prec-arg-types(lbl,p.mrec-spec(S;lbl;p);k;lbl)).
P[<k, mk-prec(lbl;t)>])
⇒ (∀x:mobj(S). P[x]))
Proof
Definitions occuring in Statement :
mobj: mobj(L),
mkinds: mKinds,
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,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
pair: <a, b>,
natural_number: $n,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
mkinds: mKinds,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_apply: x[s],
subtype_rel: A ⊆r B,
mrec: mrec(L;i),
guard: {T},
uimplies: b supposing a
Lemmas referenced :
mobj_wf,
mrec_spec_wf,
mobj-sq,
mobj-kind_wf,
mobj-label_wf,
mobj-tuple_wf,
mkinds_wf,
istype-atom,
istype-less_than,
length_wf,
mrec-spec_wf,
tuple-type_wf,
prec-arg-types_wf,
mk-prec_wf,
subtype_rel_self,
mrec_wf,
mobj-ext,
ext-eq_inversion,
subtype_rel_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :functionIsType,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :TYPEIsType,
Error :lambdaFormation_alt,
sqequalRule,
dependent_functionElimination,
Error :setIsType,
natural_numberEquality,
instantiate,
unionEquality,
cumulativity,
atomEquality,
universeEquality,
setElimination,
rename,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
Error :TYPEMemberIsType,
applyEquality,
Error :dependent_pairEquality_alt,
productEquality,
independent_isectElimination
Latex:
\mforall{}[S:MutualRectypeSpec]. \mforall{}[P:mobj(S) {}\mrightarrow{} TYPE].
((\mforall{}k:mKinds. \mforall{}lbl:\{lbl:Atom| 0 < ||mrec-spec(S;lbl;k)||\} .
\mforall{}t:tuple-type(prec-arg-types(lbl,p.mrec-spec(S;lbl;p);k;lbl)).
P[<k, mk-prec(lbl;t)>])
{}\mRightarrow{} (\mforall{}x:mobj(S). P[x]))
Date html generated:
2019_06_20-PM-02_15_38
Last ObjectModification:
2019_03_12-PM-11_13_04
Theory : tuples
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