Nuprl Lemma : es-interval-nil
∀es:EO. ∀e,e':E. [e, e'] = [] ∈ (E List) ⇐⇒ (e' <loc e) supposing loc(e) = loc(e') ∈ Id
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
nil: [],
list: T List,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
less_than': less_than'(a;b),
false: False,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
not: ¬A,
cons: [a / b],
top: Top,
guard: {T},
nat: ℕ,
le: A ≤ B,
subtract: n - m,
subtype_rel: A ⊆r B,
true: True
Latex:
\mforall{}es:EO. \mforall{}e,e':E. [e, e'] = [] \mLeftarrow{}{}\mRightarrow{} (e' <loc e) supposing loc(e) = loc(e')
Date html generated:
2016_05_16-AM-09_32_33
Last ObjectModification:
2016_01_17-PM-01_29_19
Theory : new!event-ordering
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