Nuprl Lemma : per-type-family_wf
∀[A:Type]. ∀[B:Type supposing A]. (per-type-family(B) ∈ per-function(A;a.Type))
Proof
Definitions occuring in Statement :
per-type-family: per-type-family(B),
per-function: per-function(A;a.B[a]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
per-type-family: per-type-family(B),
uimplies: b supposing a,
per-function: per-function(A;a.B[a]),
function-eq: function-eq(A;a.B[a];f;g),
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
per-function_wf_type,
equal-wf-base,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
hypothesis,
isectEquality,
cumulativity,
hypothesisEquality,
universeEquality,
introduction,
extract_by_obid,
isectElimination,
thin,
pointwiseFunctionalityForEquality,
equalityTransitivity,
equalitySymmetry,
pertypeMemberEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
isect_memberEquality,
axiomEquality,
applyEquality,
because_Cache,
lambdaEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:Type supposing A]. (per-type-family(B) \mmember{} per-function(A;a.Type))
Date html generated:
2019_06_20-AM-11_29_59
Last ObjectModification:
2018_08_22-PM-01_38_05
Theory : per!type
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