Nuprl Lemma : has-value_wf-partial
∀[A:Type]. ∀[a:partial(A)]. ((a)↓ ∈ ℙ) supposing value-type(A)
Proof
Definitions occuring in Statement :
partial: partial(T),
value-type: value-type(T),
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
partial: partial(T),
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
per-partial: per-partial(T;x;y),
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
partial_wf,
value-type_wf,
has-value-extensionality,
has-value_wf_base,
equal-wf-base,
base-partial_wf,
per-partial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
productEquality,
cumulativity
Latex:
\mforall{}[A:Type]. \mforall{}[a:partial(A)]. ((a)\mdownarrow{} \mmember{} \mBbbP{}) supposing value-type(A)
Date html generated:
2016_05_14-AM-06_09_40
Last ObjectModification:
2015_12_26-AM-11_52_14
Theory : partial_1
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