Nuprl Lemma : iseg-es-le-before-is-before
∀[es:EO]. ∀[e,x:E]. ∀[L:E List]. L = before(x) ∈ (E List) supposing L @ [x] ≤ ≤loc(e)
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-before: before(e),
es-E: E,
event_ordering: EO,
iseg: l1 ≤ l2,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iseg: l1 ≤ l2,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
or: P ∨ Q,
guard: {T},
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
subtype_rel: A ⊆r B,
true: True,
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],
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
decidable: Dec(P),
cand: A c∧ B,
squash: ↓T
Latex:
\mforall{}[es:EO]. \mforall{}[e,x:E]. \mforall{}[L:E List]. L = before(x) supposing L @ [x] \mleq{} \mleq{}loc(e)
Date html generated:
2016_05_16-AM-09_38_20
Last ObjectModification:
2016_01_17-PM-01_27_08
Theory : new!event-ordering
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