Nuprl Lemma : member-per-value
∀[x:Base]. x ∈ per-value() supposing (x)↓
Proof
Definitions occuring in Statement :
per-value: per-value(),
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
prop: ℙ,
per-set: per-set(A;a.B[a]),
per-value: per-value(),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
per-set_wf,
base_wf,
has-value_wf_base
Rules used in proof :
because_Cache,
isect_memberEquality,
hypothesisEquality,
thin,
isectElimination,
lemma_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
hypothesis,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
cumulativity,
extract_by_obid,
lambdaEquality,
independent_pairFormation,
pertypeMemberEquality
Latex:
\mforall{}[x:Base]. x \mmember{} per-value() supposing (x)\mdownarrow{}
Date html generated:
2019_06_20-AM-11_30_28
Last ObjectModification:
2018_08_07-PM-00_57_35
Theory : per!type
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