Nuprl Lemma : iterated-classrel-iff
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:A ⟶ S ⟶ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:S].
uiff(iterated_classrel(es;S;A;f;init;X;e;v);↓iterated-classrel(es;S;A;f;init;X;e;v))
Proof
Definitions occuring in Statement :
iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v),
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
squash: ↓T,
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
prop: ℙ,
guard: {T},
squash: ↓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,
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v),
cand: A c∧ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
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].
\mforall{}[v:S].
uiff(iterated\_classrel(es;S;A;f;init;X;e;v);\mdownarrow{}iterated-classrel(es;S;A;f;init;X;e;v))
Date html generated:
2016_05_16-PM-01_54_19
Last ObjectModification:
2016_01_17-PM-07_42_51
Theory : event-ordering
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