Nuprl Lemma : Regularcoset-regularset
∀A:coSet{i:l}. (cRegular(A) ⇒ regular(A))
Proof
Definitions occuring in Statement :
Regularcoset: cRegular(A),
regularset: regular(A),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
regularset: regular(A),
Regularcoset: cRegular(A),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
Regularcoset_wf,
set_wf,
setmem_wf,
mv-map_wf,
coset-relation-setrel,
coSet_wf,
subtype_rel_dep_function,
setrel_wf
Rules used in proof :
rename,
setElimination,
setEquality,
independent_isectElimination,
because_Cache,
universeEquality,
functionEquality,
lambdaEquality,
sqequalRule,
cumulativity,
instantiate,
applyEquality,
isectElimination,
extract_by_obid,
introduction,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
independent_pairFormation,
hypothesis,
cut,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}A:coSet\{i:l\}. (cRegular(A) {}\mRightarrow{} regular(A))
Date html generated:
2018_07_29-AM-10_06_57
Last ObjectModification:
2018_07_20-PM-03_25_55
Theory : constructive!set!theory
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