Nuprl Lemma : choice-principle_wf
∀[T:Type]. (ChoicePrinciple(T) ∈ 𝕌')
Proof
Definitions occuring in Statement :
choice-principle: ChoicePrinciple(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
choice-principle: ChoicePrinciple(T),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q
Lemmas referenced :
equiv_rel_true,
true_wf,
quotient_wf,
iff_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaEquality,
applyEquality,
hypothesis,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. (ChoicePrinciple(T) \mmember{} \mBbbU{}')
Date html generated:
2016_05_14-PM-09_42_14
Last ObjectModification:
2016_01_11-PM-02_11_15
Theory : continuity
Home
Index