Nuprl Lemma : altbarsep_wf
∀[T,S:Type]. (BarSep(T;S) ∈ ℙ)
Proof
Definitions occuring in Statement :
altbarsep: BarSep(T;S),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
or: P ∨ Q,
implies: P ⇒ Q,
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
altbarsep: BarSep(T;S),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
altbar_wf,
altjbar_wf,
bool_wf,
int_seg_wf,
nat_wf
Rules used in proof :
universeEquality,
instantiate,
Error :isectIsTypeImplies,
Error :isect_memberEquality_alt,
Error :inhabitedIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
unionEquality,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T,S:Type]. (BarSep(T;S) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_46_16
Last ObjectModification:
2019_06_06-AM-11_04_57
Theory : fan-theorem
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