Nuprl Lemma : State-comb-es-sv1
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[f:A ⟶ B ⟶ B]. ∀[X:EClass(A)]. ∀[init:Id ⟶ bag(B)].
(es-sv-class(es;State-comb(init;f;X))) supposing ((∀l:Id. (#(init l) ≤ 1)) and es-sv-class(es;X))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
es-sv-class: es-sv-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
State-comb: State-comb(init;f;X),
rec-combined-class-opt-1: F|X,Prior(self)?init|,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
less_than: a < b,
squash: ↓T,
true: True,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
lifting-2: lifting-2(f),
lifting2: lifting2(f;abag;bbag),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
eq_int: (i =z j),
select: L[n],
cons: [a / b],
subtract: n - m,
eclass: EClass(A[eo; e]),
es-sv-class: es-sv-class(es;X),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
ge: i ≥ j
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
(es-sv-class(es;State-comb(init;f;X))) supposing ((\mforall{}l:Id. (\#(init l) \mleq{} 1)) and es-sv-class(es;X))
Date html generated:
2016_05_17-AM-09_59_22
Last ObjectModification:
2016_01_17-PM-11_08_27
Theory : classrel!lemmas
Home
Index