Nuprl Lemma : sqntype_subtype_base
∀[A:Type]. ∀[n:ℕ]. sqntype(n;A) supposing A ⊆r Base
Proof
Definitions occuring in Statement :
sqntype: sqntype(n;T),
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
sqntype_subtype,
base_wf,
sqntype_base,
subtype_rel_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
sqequalRule,
axiomEquality,
hypothesis,
thin,
rename,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
independent_isectElimination,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[n:\mBbbN{}]. sqntype(n;A) supposing A \msubseteq{}r Base
Date html generated:
2019_06_20-AM-11_34_09
Last ObjectModification:
2018_08_17-PM-03_55_26
Theory : int_1
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