Nuprl Lemma : member-per-and
∀[A:Type]. ∀[B:Type supposing A]. ∀[a:A]. ∀[b:B]. (<a, b> ∈ per-and(A;B))
Proof
Definitions occuring in Statement :
per-and: per-and(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
pair: <a, b>,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
per-and: per-and(A;B),
guard: {T},
per-type-family: per-type-family(B)
Lemmas referenced :
isect_subtype_rel_trivial,
subtype_rel_self,
member-per-product,
per-type-family_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
hypothesisEquality,
applyEquality,
thin,
sqequalRule,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
because_Cache,
lambdaEquality,
universeEquality,
independent_isectElimination,
independent_pairFormation,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:Type supposing A]. \mforall{}[a:A]. \mforall{}[b:B]. (<a, b> \mmember{} per-and(A;B))
Date html generated:
2019_06_20-AM-11_30_23
Last ObjectModification:
2018_08_22-PM-01_47_22
Theory : per!type
Home
Index