Nuprl Lemma : cut-order-iff1
∀[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)) ∨ ((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'),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T
Lemmas :
or_wf,
equal_wf,
es-E-interface_wf,
es-causl_wf,
event-ordering+_subtype,
fset-member_wf-cut,
cut-of_wf,
fset-singleton_wf,
assert_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
top_wf,
subtype_top,
eclass-val_wf2,
es-prior-interface_wf,
iff_wf,
squash_wf,
true_wf,
es-cut_wf,
sys-antecedent_wf,
eclass_wf,
event-ordering+_wf,
cut-of-singleton,
iff_weakening_equal,
sq_stable__es-causle,
bool_wf,
es-eq-E_wf,
equal-wf-T-base,
member-fset-singleton,
es-eq_wf-interface,
fset-member_wf,
member-fset-union,
fset-union_wf,
es-causle_weakening_eq,
es-causle_wf,
and_wf,
bnot_wf,
not_wf,
false_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
assert-es-eq-E-2,
iff_transitivity,
iff_weakening_uiff,
es-causl_transitivity2,
es-causl_irreflexivity
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{} ((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_04_23
Last ObjectModification:
2015_02_04-PM-06_07_35
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