Nuprl Lemma : member-tagged+-right
∀[T,B:Type]. ∀[a:Atom]. ∀[p:T |+ a:B]. p ∈ T supposing ¬(p.tag = a ∈ Atom)
Proof
Definitions occuring in Statement :
tagged-tag: x.tag,
tagged+: T |+ z:B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
atom: Atom,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
tagged+_subtype_rel,
not_wf,
equal_wf,
tagged-tag_wf2,
tagged+_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
atomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T,B:Type]. \mforall{}[a:Atom]. \mforall{}[p:T |+ a:B]. p \mmember{} T supposing \mneg{}(p.tag = a)
Date html generated:
2016_05_15-PM-06_49_29
Last ObjectModification:
2015_12_27-AM-11_45_32
Theory : general
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