Nuprl Lemma : fs-in-subtype_wf
∀[K:RngSig]. ∀[S,T:Type]. ∀[f:formal-sum(K;S)]. (fs-in-subtype(K;S;T;f) ∈ ℙ) supposing strong-subtype(T;S)
Proof
Definitions occuring in Statement :
fs-in-subtype: fs-in-subtype(K;S;T;f),
formal-sum: formal-sum(K;S),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
fs-in-subtype: fs-in-subtype(K;S;T;f),
member: t ∈ T,
so_lambda: λ2x.t[x],
pi2: snd(t),
uiff: uiff(P;Q),
and: P ∧ Q,
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
fs-predicate_wf,
strong-subtype-iff-respects-equality,
rng_car_wf,
formal-sum_wf,
strong-subtype_wf,
istype-universe,
rng_sig_wf,
equal-wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
productElimination,
because_Cache,
hypothesis,
independent_isectElimination,
productIsType,
universeIsType,
instantiate,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[K:RngSig]. \mforall{}[S,T:Type].
\mforall{}[f:formal-sum(K;S)]. (fs-in-subtype(K;S;T;f) \mmember{} \mBbbP{}) supposing strong-subtype(T;S)
Date html generated:
2019_10_31-AM-06_29_06
Last ObjectModification:
2019_08_19-PM-01_16_34
Theory : linear!algebra
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