Nuprl Lemma : in-first-eclass
∀[Info,A:Type]. ∀Xs:EClass(A) List. ∀es:EO+(Info). ∀e:E. (↑e ∈b first-eclass(Xs) ⇐⇒ (∃X∈Xs. ↑e ∈b X))
Proof
Definitions occuring in Statement :
first-eclass: first-eclass(Xs),
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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
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,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b],
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
int_iseg: {i...j},
cand: A c∧ B,
first-eclass: first-eclass(Xs),
in-eclass: e ∈b X,
eq_int: (i =z j),
eclass: EClass(A[eo; e]),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
true: True,
rev_uimplies: rev_uimplies(P;Q),
sq_type: SQType(T),
bnot: ¬bb,
l_exists: (∃x∈L. P[x]),
nequal: a ≠ b ∈ T ,
select: L[n]
Latex:
\mforall{}[Info,A:Type].
\mforall{}Xs:EClass(A) List. \mforall{}es:EO+(Info). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} first-eclass(Xs) \mLeftarrow{}{}\mRightarrow{} (\mexists{}X\mmember{}Xs. \muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_16-PM-10_34_27
Last ObjectModification:
2016_01_17-PM-07_28_56
Theory : event-ordering
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