Nuprl Lemma : basic-formal-sum-strong-subtype
∀[K:RngSig]. ∀[S,T:Type]. strong-subtype(basic-formal-sum(K;S);basic-formal-sum(K;T)) supposing strong-subtype(S;T)
Proof
Definitions occuring in Statement :
basic-formal-sum: basic-formal-sum(K;S),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
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,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
strong-subtype-bag,
strong-subtype-product,
strong-subtype-self,
strong-subtype_witness,
bag_wf,
rng_car_wf,
strong-subtype_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,
because_Cache,
independent_isectElimination,
hypothesisEquality,
hypothesis,
productEquality,
independent_functionElimination,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[K:RngSig]. \mforall{}[S,T:Type].
strong-subtype(basic-formal-sum(K;S);basic-formal-sum(K;T)) supposing strong-subtype(S;T)
Date html generated:
2019_10_31-AM-06_28_17
Last ObjectModification:
2019_08_15-PM-02_28_28
Theory : linear!algebra
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