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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