Nuprl Lemma : per-or-family_wf
∀[A,B:Type]. (per-or-family(A;B) ∈ per-function(per-value();a.Type))
Proof
Definitions occuring in Statement :
per-value: per-value(),
per-or-family: per-or-family(A;B),
per-function: per-function(A;a.B[a]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
per-function: per-function(A;a.B[a]),
function-eq: function-eq(A;a.B[a];f;g),
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
per-or-family: per-or-family(A;B),
uand: uand(A;B),
has-value: (a)↓,
top: Top
Lemmas referenced :
per-function_wf_type,
per-value_wf,
equal-wf-base,
base_wf,
per-value_subtype_base,
subtype_base_sq,
subtype_rel_self,
equal_wf,
per-value-property,
has-value_wf_base,
is-exception_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
pointwiseFunctionalityForEquality,
equalityTransitivity,
equalitySymmetry,
pertypeMemberEquality,
sqequalRule,
hypothesisEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
universeEquality,
applyEquality,
instantiate,
cumulativity,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
lambdaFormation,
axiomSqleEquality,
divergentSqle,
sqleReflexivity,
isaxiomCases,
axiomSqEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[A,B:Type]. (per-or-family(A;B) \mmember{} per-function(per-value();a.Type))
Date html generated:
2019_06_20-AM-11_30_30
Last ObjectModification:
2018_08_22-PM-02_04_42
Theory : per!type
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