Nuprl Lemma : sqntype_wf
∀[T:Type]. ∀[n:ℕ]. (sqntype(n;T) ∈ ℙ)
Proof
Definitions occuring in Statement :
sqntype: sqntype(n;T),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sqntype: sqntype(n;T),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
base_wf,
equal-wf-base,
sqequal_n_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
functionEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. (sqntype(n;T) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_33_55
Last ObjectModification:
2018_08_17-PM-03_30_59
Theory : int_1
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