Nuprl Lemma : prior-as-rec-bind-class-in-property
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[x,a:bag(A) + (bag(A)?)]. ∀[es:EO+(Info)]. ∀[e:E].
∀[w:bag(A) + (bag(A)?)]. (¬w ∈ prior-as-rec-bind-class-in(X;a)(e)) supposing a ∈ prior-as-rec-bind-class-in(X;x)(e)
Proof
Definitions occuring in Statement :
prior-as-rec-bind-class-in: prior-as-rec-bind-class-in(X;i),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
unit: Unit,
union: left + right,
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
not: ¬A,
prior-as-rec-bind-class-in: prior-as-rec-bind-class-in(X;i),
uiff: uiff(P;Q),
and: P ∧ Q,
false: False,
disjoint-union-comb: X (+) Y,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
sq_or: a ↓∨ b,
squash: ↓T,
or: P ∨ Q,
simple-comb-1: F|X|,
simple-comb: simple-comb(F;Xs),
select: L[n],
cons: [a / b],
classrel: v ∈ X(e),
lifting-1: lifting-1(f),
lifting1: lifting1(f;b),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
null-class: Null,
eclass: EClass(A[eo; e]),
parallel-class: X || Y,
eclass-compose2: eclass-compose2(f;X;Y),
iff: P ⇐⇒ Q
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[x,a:bag(A) + (bag(A)?)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[w:bag(A) + (bag(A)?)]. (\mneg{}w \mmember{} prior-as-rec-bind-class-in(X;a)(e))
supposing a \mmember{} prior-as-rec-bind-class-in(X;x)(e)
Date html generated:
2016_05_17-AM-00_29_56
Last ObjectModification:
2015_12_29-AM-00_48_23
Theory : event-ordering
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