Nuprl Lemma : member-of-tagged+2
∀[T,B:Type]. ∀[tg,a:Atom]. ∀[x:T]. mk-tagged(tg;x) ∈ a:B |+ tg:T supposing ¬(tg = a ∈ Atom)
Proof
Definitions occuring in Statement :
mk-tagged: mk-tagged(tg;x),
tagged+: T |+ z:B,
tag-case: z:T,
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,
tagged+: T |+ z:B,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
false: False,
top: Top,
bfalse: ff
Lemmas referenced :
mk-tagged_wf_unequal,
assert_of_eq_atom,
iff_transitivity,
not_wf,
equal-wf-base,
atom_subtype_base,
assert_wf,
eq_atom_wf,
bnot_wf,
iff_weakening_uiff,
assert_of_bnot,
mk-tagged_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
isect_memberEquality,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
sqequalRule,
extract_by_obid,
isectElimination,
hypothesisEquality,
because_Cache,
hypothesis,
productElimination,
independent_pairFormation,
independent_isectElimination,
atomEquality,
applyEquality,
independent_functionElimination,
lambdaFormation,
impliesFunctionality,
equalitySymmetry,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
universeEquality
Latex:
\mforall{}[T,B:Type]. \mforall{}[tg,a:Atom]. \mforall{}[x:T]. mk-tagged(tg;x) \mmember{} a:B |+ tg:T supposing \mneg{}(tg = a)
Date html generated:
2018_05_21-PM-08_43_33
Last ObjectModification:
2017_07_26-PM-06_07_30
Theory : general
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