Nuprl Lemma : es-interval-less-sq
∀[es:EO]. ∀[e,e':E]. [e, e'] ~ [e, pred(e')] @ [e'] supposing (e <loc e')
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-locl: (e <loc e'),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
append: as @ bs,
cons: [a / b],
nil: [],
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
es-before: before(e),
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
top: Top,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-interval: [e, e']
Latex:
\mforall{}[es:EO]. \mforall{}[e,e':E]. [e, e'] \msim{} [e, pred(e')] @ [e'] supposing (e <loc e')
Date html generated:
2016_05_16-AM-09_32_58
Last ObjectModification:
2015_12_28-PM-09_48_08
Theory : new!event-ordering
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