Nuprl Lemma : cut-order-iff
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀a,b:E(X).
(a ≤(X;f) b
⇐⇒ (a = b ∈ E(X))
∨ (((¬(loc(f b) = loc(b) ∈ Id)) ∧ (f b < b)) ∧ a ≤(X;f) f b)
∨ ((↑b ∈b prior(X)) ∧ a ≤(X;f) prior(X)(b)))
Proof
Definitions occuring in Statement :
cut-order: a ≤(X;f) b,
es-prior-interface: prior(X),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-causl: (e < e'),
es-loc: loc(e),
Id: Id,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T
Lemmas :
cut-order-iff1,
cut-order_wf,
iff_wf,
or_wf,
equal_wf,
es-E-interface_wf,
es-causl_wf,
event-ordering+_subtype,
assert_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
subtype_top,
eclass-val_wf2,
es-prior-interface_wf,
not_wf,
Id_wf,
es-loc_wf,
sys-antecedent_wf,
eclass_wf,
sq_stable__es-causle,
decidable__equal_Id,
is-prior-interface,
es-E-interface-property,
es-locl_wf,
cut-order_weakening-le,
es-le-prior-interface-val,
cut-order_transitivity
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X). \mforall{}a,b:E(X).
(a \mleq{}(X;f) b
\mLeftarrow{}{}\mRightarrow{} (a = b)
\mvee{} (((\mneg{}(loc(f b) = loc(b))) \mwedge{} (f b < b)) \mwedge{} a \mleq{}(X;f) f b)
\mvee{} ((\muparrow{}b \mmember{}\msubb{} prior(X)) \mwedge{} a \mleq{}(X;f) prior(X)(b)))
Date html generated:
2015_07_21-PM-04_06_02
Last ObjectModification:
2015_01_27-PM-05_49_38
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