Nuprl Lemma : dfan_wf
∀[T:Type]. (Fan_d(T) ∈ ℙ')
Proof
Definitions occuring in Statement :
dfan: Fan_d(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dfan: Fan_d(T),
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
all_wf,
list_wf,
dbar_wf,
ubar_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
hypothesis,
universeEquality,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. (Fan\_d(T) \mmember{} \mBbbP{}')
Date html generated:
2016_05_14-PM-04_09_22
Last ObjectModification:
2015_12_26-PM-07_54_35
Theory : fan-theorem
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