Nuprl Lemma : Regularset_wf
∀[A:Set{i:l}]. (Regular(A) ∈ ℙ{i''})
Proof
Definitions occuring in Statement :
Regularset: Regular(A),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
guard: {T},
exists: ∃x:A. B[x],
uimplies: b supposing a,
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
Regularset: Regular(A),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
onto-map_wf,
exists_wf,
set_wf,
subtype_rel_self,
subtype_rel_sets,
subtype_rel_dep_function,
setsubset-iff,
transitive-set-iff,
mv-map_wf,
set-relation-on_wf,
setmem_wf,
Set_wf,
all_wf,
transitive-set_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_isectElimination,
promote_hyp,
allFunctionality,
independent_functionElimination,
productElimination,
dependent_functionElimination,
functionExtensionality,
rename,
setElimination,
lambdaFormation,
setEquality,
because_Cache,
functionEquality,
instantiate,
universeEquality,
cumulativity,
lambdaEquality,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:Set\{i:l\}]. (Regular(A) \mmember{} \mBbbP{}\{i''\})
Date html generated:
2018_05_29-PM-01_52_43
Last ObjectModification:
2018_05_25-PM-02_02_54
Theory : constructive!set!theory
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