Nuprl Lemma : iterated_classrel-exists
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:A ⟶ S ⟶ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].
↓∃v:S. iterated_classrel(es;S;A;f;init;X;e;v) supposing ↓∃s:S. s ↓∈ init loc(e)
Proof
Definitions occuring in Statement :
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
uall: ∀[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},
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
le: A ≤ B,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
cand: A c∧ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-E: E,
es-base-E: es-base-E(es),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mdownarrow{}\mexists{}v:S. iterated\_classrel(es;S;A;f;init;X;e;v) supposing \mdownarrow{}\mexists{}s:S. s \mdownarrow{}\mmember{} init loc(e)
Date html generated:
2016_05_16-PM-01_48_11
Last ObjectModification:
2016_01_17-PM-07_46_26
Theory : event-ordering
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