Nuprl Lemma : basic-formal-sum-subtype
∀[K:RngSig]. ∀[S,T:Type]. basic-formal-sum(K;S) ⊆r basic-formal-sum(K;T) supposing S ⊆r T
Proof
Definitions occuring in Statement :
basic-formal-sum: basic-formal-sum(K;S),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
subtype_rel_bag,
rng_car_wf,
subtype_rel_product,
subtype_rel_wf,
istype-universe,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
lambdaEquality_alt,
universeIsType,
because_Cache,
lambdaFormation_alt,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[K:RngSig]. \mforall{}[S,T:Type]. basic-formal-sum(K;S) \msubseteq{}r basic-formal-sum(K;T) supposing S \msubseteq{}r T
Date html generated:
2019_10_31-AM-06_28_14
Last ObjectModification:
2019_08_15-PM-02_17_07
Theory : linear!algebra
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