Nuprl Lemma : choicef_wf
∀[xm:XM]. ∀[T:Type]. ∀[P:T ⟶ ℙ]. ∈x:T. P[x] ∈ T supposing ∃a:T. P[a]
Proof
Definitions occuring in Statement :
choicef: ∈x:T. P[x],
xmiddle: XM,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
exists: ∃x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
choicef: ∈x:T. P[x],
xmiddle: XM,
decidable: Dec(P),
exists: ∃x:A. B[x],
member: t ∈ T,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
implies: P ⇒ Q,
not: ¬A,
false: False
Lemmas referenced :
exists_wf,
xmiddle_wf,
set_wf,
or_wf,
not_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalHypSubstitution,
sqequalRule,
Error :productIsType,
Error :universeIsType,
hypothesisEquality,
cut,
applyEquality,
hypothesis,
thin,
lambdaEquality,
universeEquality,
introduction,
extract_by_obid,
isectElimination,
Error :functionIsType,
because_Cache,
functionEquality,
cumulativity,
Error :isect_memberFormation_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionExtensionality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
setElimination,
rename,
voidElimination,
productElimination,
dependent_set_memberFormation
Latex:
\mforall{}[xm:XM]. \mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mmember{}x:T. P[x] \mmember{} T supposing \mexists{}a:T. P[a]
Date html generated:
2019_06_20-AM-11_17_55
Last ObjectModification:
2018_09_26-AM-10_25_02
Theory : core_2
Home
Index