Nuprl Lemma : base-member-of-tagged+
∀[T,B:Type]. ∀[tg,a:Atom]. ∀[x:Base].
(mk-tagged(tg;x) ∈ T |+ a:B) supposing ((¬(tg = a ∈ Atom)) and (mk-tagged(tg;x) ∈ T))
Proof
Definitions occuring in Statement :
mk-tagged: mk-tagged(tg;x),
tagged+: T |+ z:B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
base: Base,
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 ,
bfalse: ff,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
uiff: uiff(P;Q),
prop: ℙ,
rev_implies: P ⇐ Q,
false: False,
top: Top
Lemmas referenced :
mk-tagged_wf_unequal,
iff_transitivity,
not_wf,
equal-wf-base,
atom_subtype_base,
assert_wf,
eq_atom_wf,
bnot_wf,
assert_of_eq_atom,
iff_weakening_uiff,
assert_of_bnot,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
isect_memberEquality,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
hypothesis,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
independent_isectElimination,
atomEquality,
applyEquality,
because_Cache,
independent_functionElimination,
independent_pairFormation,
lambdaFormation,
impliesFunctionality,
productElimination,
equalitySymmetry,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
baseApply,
closedConclusion,
baseClosed,
universeEquality
Latex:
\mforall{}[T,B:Type]. \mforall{}[tg,a:Atom]. \mforall{}[x:Base].
(mk-tagged(tg;x) \mmember{} T |+ a:B) supposing ((\mneg{}(tg = a)) and (mk-tagged(tg;x) \mmember{} T))
Date html generated:
2018_05_21-PM-08_43_46
Last ObjectModification:
2017_07_26-PM-06_07_43
Theory : general
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