Nuprl Lemma : sys-antecedent-filter-image
∀[Info,A,B:Type]. ∀[g:A ⟶ bag(B)]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[f:sys-antecedent(es;X)].
f ∈ sys-antecedent(es;g[X]) supposing ∀a:E(X). ((¬((f a) = a ∈ E(X))) ⇒ (#(g X(a)) = 1 ∈ ℤ) ⇒ (#(g X(f a)) = 1 ∈ ℤ))
Proof
Definitions occuring in Statement :
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
es-filter-image: f[X],
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
sys-antecedent: sys-antecedent(es;Sys),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
es-E-interface: E(X),
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[g:A {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[f:sys-antecedent(es;X)].
f \mmember{} sys-antecedent(es;g[X])
supposing \mforall{}a:E(X). ((\mneg{}((f a) = a)) {}\mRightarrow{} (\#(g X(a)) = 1) {}\mRightarrow{} (\#(g X(f a)) = 1))
Date html generated:
2016_05_17-AM-08_08_28
Last ObjectModification:
2016_01_17-PM-02_45_34
Theory : event-ordering
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