Nuprl Lemma : first-eclass-val
∀[Info,A:Type].
∀Xs:EClass(A) List. ∀es:EO+(Info). ∀e:E.
(∃X∈Xs. (↑e ∈b X) ∧ (first-eclass(Xs)(e) = X(e) ∈ A)) supposing ↑e ∈b first-eclass(Xs)
Proof
Definitions occuring in Statement :
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_exists: (∃x∈L. P[x]),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
top: Top,
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
first-eclass: first-eclass(Xs),
in-eclass: e ∈b X,
eq_int: (i =z j),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
decidable: Dec(P),
or: P ∨ Q,
l_exists: (∃x∈L. P[x]),
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
true: True,
guard: {T},
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
select: L[n],
cons: [a / b],
cand: A c∧ B,
eclass-val: X(e),
eclass: EClass(A[eo; e]),
nat: ℕ,
ge: i ≥ j ,
colength: colength(L),
nil: [],
it: ⋅,
sq_type: SQType(T),
bool: 𝔹,
unit: Unit,
btrue: tt,
rev_uimplies: rev_uimplies(P;Q),
bnot: ¬bb,
rev_implies: P ⇐ Q,
nequal: a ≠ b ∈ T
Latex:
\mforall{}[Info,A:Type].
\mforall{}Xs:EClass(A) List. \mforall{}es:EO+(Info). \mforall{}e:E.
(\mexists{}X\mmember{}Xs. (\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (first-eclass(Xs)(e) = X(e))) supposing \muparrow{}e \mmember{}\msubb{} first-eclass(Xs)
Date html generated:
2016_05_16-PM-10_34_50
Last ObjectModification:
2016_01_17-PM-07_40_18
Theory : event-ordering
Home
Index