Nuprl Lemma : es-prior-interface-vals-property
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A)]. ∀[e:E].
(X(<e) = if e ∈b prior(X) then X(<prior(X)(e)) @ [X(prior(X)(e))] else [] fi ∈ (A List))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-prior-interface-vals: 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: [],
list: T List,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ 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,
es-prior-interface-vals: X(<e),
es-before: before(e),
iff: P ⇐⇒ Q,
mapfilter: mapfilter(f;P;L),
rev_implies: P ⇐ Q,
true: True,
rev_uimplies: rev_uimplies(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
(X(<e) = if e \mmember{}\msubb{} prior(X) then X(<prior(X)(e)) @ [X(prior(X)(e))] else [] fi )
Date html generated:
2016_05_17-AM-06_28_24
Last ObjectModification:
2016_01_17-PM-06_40_37
Theory : event-ordering
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