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)
Lemmas :
all_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
not_wf,
equal_wf,
equal-wf-T-base,
bag-size_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
nat_wf,
es-E-interface-property,
sys-antecedent_wf,
eclass_wf,
bag_wf,
es-filter-image_wf,
subtype_rel_dep_function,
subtype_rel_bag,
es-is-filter-image,
assert_wf,
decidable__equal_es-E-interface,
iff_weakening_equal,
es-E-filter-image,
es-causle_wf
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:
2015_07_21-PM-04_19_44
Last ObjectModification:
2015_02_04-PM-06_05_43
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