Nuprl Lemma : assert-es-ble-base
∀es:EO. ∀e,e':es-base-E(es). (↑e ≤loc e' ⇐⇒ ((loc(e) = loc(e') ∈ Id) ∧ (e < e')) ∨ (e = e' ∈ es-base-E(es)))
Proof
Definitions occuring in Statement :
es-ble: e ≤loc e',
es-causl: (e < e'),
es-loc: loc(e),
es-base-E: es-base-E(es),
event_ordering: EO,
Id: Id,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
es-ble: e ≤loc e',
es-bless: e <loc e',
es-blocl: es-blocl(es;e1;e2),
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
guard: {T},
or: P ∨ Q,
decidable: Dec(P),
not: ¬A,
false: False,
cand: A c∧ B
Latex:
\mforall{}es:EO. \mforall{}e,e':es-base-E(es). (\muparrow{}e \mleq{}loc e' \mLeftarrow{}{}\mRightarrow{} ((loc(e) = loc(e')) \mwedge{} (e < e')) \mvee{} (e = e'))
Date html generated:
2016_05_16-AM-09_29_14
Last ObjectModification:
2015_12_28-PM-09_51_45
Theory : new!event-ordering
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