Nuprl Lemma : regularExtension
∀a:Set{i:l}. ∃r:Set{i:l}. ((a ⊆ r) ∧ regular(r))
Proof
Definitions occuring in Statement :
regularset: regular(A),
setsubset: (a ⊆ b),
Set: Set{i:l},
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
cand: A c∧ B,
prop: ℙ,
implies: P ⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
Set_wf,
regularset_wf,
setsubset_wf,
Regularset-regularset,
RegularExtension
Rules used in proof :
isectElimination,
cumulativity,
productEquality,
independent_functionElimination,
promote_hyp,
independent_pairFormation,
dependent_pairFormation,
productElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}a:Set\{i:l\}. \mexists{}r:Set\{i:l\}. ((a \msubseteq{} r) \mwedge{} regular(r))
Date html generated:
2018_05_29-PM-01_53_06
Last ObjectModification:
2018_05_24-PM-03_28_23
Theory : constructive!set!theory
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