Nuprl Lemma : has-valueall-pair
∀[a,b:Base]. uiff(has-valueall(<a, b>);has-valueall(a) ∧ has-valueall(b))
Proof
Definitions occuring in Statement :
has-valueall: has-valueall(a),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
pair: <a, b>,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-valueall: has-valueall(a),
top: Top,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
has-value: (a)↓,
prop: ℙ,
evalall: evalall(t)
Lemmas referenced :
base_wf,
has-valueall_wf_base,
and_wf,
is-exception_wf,
has-value_wf_base,
evalall-pair
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
independent_pairFormation,
callbyvalueCallbyvalue,
callbyvalueReduce,
productElimination,
independent_pairEquality,
axiomSqleEquality,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
callbyvalueIspair,
divergentSqle,
sqleReflexivity,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[a,b:Base]. uiff(has-valueall(<a, b>);has-valueall(a) \mwedge{} has-valueall(b))
Date html generated:
2016_05_13-PM-03_25_28
Last ObjectModification:
2016_01_14-PM-06_45_22
Theory : call!by!value_1
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