Nuprl Lemma : altfan_wf
∀[T:Type]. (Fan(T) ∈ ℙ')
Proof
Definitions occuring in Statement :
altfan: Fan(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
implies: P ⇒ Q,
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
altfan: Fan(T),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
altubar_wf,
altbar_wf,
bool_wf,
int_seg_wf,
nat_wf
Rules used in proof :
universeEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
cumulativity,
functionEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. (Fan(T) \mmember{} \mBbbP{}')
Date html generated:
2019_06_20-PM-02_46_02
Last ObjectModification:
2019_06_06-AM-10_58_45
Theory : fan-theorem
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