Nuprl Lemma : tl-es-le-before
∀es:EO. ∀e,e':E. ((e' ∈ tl(≤loc(e))) ⇐⇒ e' ≤loc e ∧ (¬↑first(e')))
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-le: e ≤loc e' ,
es-first: first(e),
es-E: E,
event_ordering: EO,
l_member: (x ∈ l),
tl: tl(l),
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat: ℕ,
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
es-le-before: ≤loc(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],
bfalse: ff,
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b],
es-le: e ≤loc e' ,
cand: A c∧ B
Latex:
\mforall{}es:EO. \mforall{}e,e':E. ((e' \mmember{} tl(\mleq{}loc(e))) \mLeftarrow{}{}\mRightarrow{} e' \mleq{}loc e \mwedge{} (\mneg{}\muparrow{}first(e')))
Date html generated:
2016_05_16-AM-09_35_19
Last ObjectModification:
2016_01_17-PM-01_28_54
Theory : new!event-ordering
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