Nuprl Lemma : per-partial-reflex
∀[T:Type]. ∀[x:base-partial(T)]. per-partial(T;x;x)
Proof
Definitions occuring in Statement :
per-partial: per-partial(T;x;y),
base-partial: base-partial(T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
base-partial: base-partial(T),
per-partial: per-partial(T;x;y),
and: P ∧ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
has-value_wf_base,
base-partial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
independent_pairFormation,
hypothesis,
sqequalRule,
axiomSqleEquality,
lemma_by_obid,
isectElimination,
hypothesisEquality,
because_Cache,
productElimination,
independent_isectElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:base-partial(T)]. per-partial(T;x;x)
Date html generated:
2016_05_14-AM-06_09_21
Last ObjectModification:
2015_12_26-AM-11_52_26
Theory : partial_1
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