Nuprl Lemma : es-interface-predecessors-step-sq
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(≤(X)(e) ~ if e ∈b prior(X) then ≤(X)(prior(X)(e)) else [] fi @ if e ∈b X then [e] else [] fi )
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-predecessors: ≤(X)(e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
append: as @ bs,
cons: [a / b],
nil: [],
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
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,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-E-interface: E(X)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\mleq{}(X)(e) \msim{} if e \mmember{}\msubb{} prior(X) then \mleq{}(X)(prior(X)(e)) else [] fi @ if e \mmember{}\msubb{} X then [e] else [] fi )
Date html generated:
2016_05_17-AM-06_53_36
Last ObjectModification:
2016_01_17-PM-06_34_48
Theory : event-ordering
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