Nuprl Lemma : bag-maximal?-single
∀[T:Type]. ∀[R:T ⟶ T ⟶ 𝔹]. ∀[v,x:T]. uiff(↑bag-maximal?({v};x;R);↑(R x v))
Proof
Definitions occuring in Statement :
bag-maximal?: bag-maximal?(bg;x;R),
single-bag: {x},
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
single-bag: {x},
bag-maximal?: bag-maximal?(bg;x;R),
bag-accum: bag-accum(v,x.f[v; x];init;bs),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
list_accum_cons_lemma,
list_accum_nil_lemma,
assert_witness,
assert_wf,
bag-maximal?_wf,
single-bag_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
independent_pairFormation,
isect_memberFormation,
introduction,
isectElimination,
applyEquality,
hypothesisEquality,
independent_functionElimination,
because_Cache,
functionEquality,
universeEquality,
productElimination,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}]. \mforall{}[v,x:T]. uiff(\muparrow{}bag-maximal?(\{v\};x;R);\muparrow{}(R x v))
Date html generated:
2016_05_15-PM-02_30_29
Last ObjectModification:
2015_12_27-AM-09_48_51
Theory : bags
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