Nuprl Lemma : es-interface-val-disjoint
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[Xs:EClass(A) List].
∀[X:EClass(A)]. ∀[e:E]. first-eclass(Xs)(e) = X(e) ∈ A supposing ↑e ∈b X supposing (X ∈ Xs)
supposing (∀X∈Xs.(∀Y∈Xs.(X = Y ∈ EClass(A)) ∨ X ⋂ Y = 0))
Proof
Definitions occuring in Statement :
es-interface-disjoint: X ⋂ Y = 0,
first-eclass: first-eclass(Xs),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
l_all: (∀x∈L.P[x]),
l_member: (x ∈ l),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
prop: ℙ,
top: Top,
so_apply: x[s],
exists: ∃x:A. B[x],
l_exists: (∃x∈L. P[x]),
squash: ↓T,
true: True,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
less_than: a < b,
es-interface-disjoint: X ⋂ Y = 0,
cand: A c∧ B
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[Xs:EClass(A) List].
\mforall{}[X:EClass(A)]. \mforall{}[e:E]. first-eclass(Xs)(e) = X(e) supposing \muparrow{}e \mmember{}\msubb{} X supposing (X \mmember{} Xs)
supposing (\mforall{}X\mmember{}Xs.(\mforall{}Y\mmember{}Xs.(X = Y) \mvee{} X \mcap{} Y = 0))
Date html generated:
2016_05_16-PM-10_49_54
Last ObjectModification:
2016_01_17-PM-07_19_59
Theory : event-ordering
Home
Index