Nuprl Lemma : set-axiom-of-choice_wf
Set-AC ∈ ℙ'
Proof
Definitions occuring in Statement :
set-axiom-of-choice: Set-AC,
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
set-axiom-of-choice: Set-AC,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s],
guard: {T},
uimplies: b supposing a
Lemmas referenced :
all_wf,
exists_wf,
ext-eq_wf,
equal_wf,
ext-eq_inversion,
subtype_rel_weakening
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
universeEquality,
lambdaEquality,
functionEquality,
cumulativity,
hypothesisEquality,
applyEquality,
functionExtensionality,
because_Cache,
hypothesis,
independent_isectElimination
Latex:
Set-AC \mmember{} \mBbbP{}'
Date html generated:
2017_04_14-AM-07_37_38
Last ObjectModification:
2017_02_27-PM-03_09_52
Theory : subtype_1
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