Nuprl Lemma : es-interval-open-interval
∀[es:EO]. ∀[e,e':E]. [e', e] = (if e' <loc e then [e'] else [] fi @ (e', e) @ [e]) ∈ (E List) supposing e' ≤loc e
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-interval: [e, e'],
es-bless: e <loc e',
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-open-interval: (e, e'),
es-interval: [e, e'],
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
es-le-before: ≤loc(e),
true: True,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[es:EO]. \mforall{}[e,e':E].
[e', e] = (if e' <loc e then [e'] else [] fi @ (e', e) @ [e]) supposing e' \mleq{}loc e
Date html generated:
2016_05_16-AM-09_34_29
Last ObjectModification:
2016_01_17-PM-01_33_20
Theory : new!event-ordering
Home
Index