Nuprl Lemma : has-valueall-single
∀[a:Base]. uiff(has-valueall(a);has-valueall([a]))
Proof
Definitions occuring in Statement :
cons: [a / b]
,
nil: []
,
has-valueall: has-valueall(a)
,
uiff: uiff(P;Q)
,
uall: ∀[x:A]. B[x]
,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
has-valueall: has-valueall(a)
,
has-value: (a)↓
,
prop: ℙ
,
cand: A c∧ B
,
nil: []
,
evalall: evalall(t)
,
it: ⋅
Lemmas referenced :
is-exception_wf,
has-value_wf_base,
has-valueall-cons,
base_wf,
has-valueall_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalRule,
sqequalHypSubstitution,
axiomSqleEquality,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
baseApply,
closedConclusion,
baseClosed,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
divergentSqle,
sqleReflexivity
Latex:
\mforall{}[a:Base]. uiff(has-valueall(a);has-valueall([a]))
Date html generated:
2016_05_14-AM-06_26_08
Last ObjectModification:
2016_01_14-PM-08_26_49
Theory : list_0
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