Nuprl Lemma : State-comb-total
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
es-total-class(es;State-comb(init;f;X)) supposing ∀l:Id. (1 ≤ #(init l))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
es-total-class: es-total-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)
Lemmas :
State-comb-exists,
es-loc_wf,
decidable__lt,
bag-size_wf,
event-ordering+_subtype,
nat_wf,
false_wf,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel,
bag-member-iff-size,
State-comb_wf,
eclass_wf,
es-E_wf,
decidable__le,
not-le-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-associates,
add-zero,
le-add-cancel2,
less_than_wf,
class-ap_wf,
all_wf,
Id_wf,
le_wf,
event-ordering+_wf,
bag_wf
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)].
es-total-class(es;State-comb(init;f;X)) supposing \mforall{}l:Id. (1 \mleq{} \#(init l))
Date html generated:
2015_07_22-PM-00_20_58
Last ObjectModification:
2015_01_28-AM-10_12_42
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