Nuprl Lemma : State3-state-class3
∀[Info,A1,A2,A3,S:Type]. ∀[init:Id ─→ S]. ∀[tr1:Id ─→ A1 ─→ S ─→ S]. ∀[X1:EClass(A1)]. ∀[tr2:Id ─→ A2 ─→ S ─→ S].
∀[X2:EClass(A2)]. ∀[tr3:Id ─→ A3 ─→ S ─→ S]. ∀[X3:EClass(A3)].
(State3(init;tr1;X1;tr2;X2;tr3;X3) = state-class3(init;tr1;X1;tr2;X2;tr3;X3) ∈ EClass(S))
Proof
Definitions occuring in Statement :
State3: State3(init;tr1;X1;tr2;X2;tr3;X3),
state-class3: state-class3(init;tr1;X1;tr2;X2;tr3;X3),
eclass: EClass(A[eo; e]),
Id: Id,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
eclass_wf,
es-E_wf,
event-ordering+_subtype,
State-loc-comb-is-loop-class-state,
single-bag_wf,
disjoint-union-tr_wf,
disjoint-union-comb_wf,
loop-class-state_wf,
parallel-class_wf,
eclass1_wf,
iff_weakening_equal,
event-ordering+_wf,
Id_wf,
bag-combine_wf,
top_wf,
bag-map_wf,
bag-append_wf,
squash_wf,
true_wf,
bag_wf,
eta_conv,
es-loc_wf,
bag-map-append,
bag-combine-single-right-as-map,
bag-map-map
Latex:
\mforall{}[Info,A1,A2,A3,S:Type]. \mforall{}[init:Id {}\mrightarrow{} S]. \mforall{}[tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X1:EClass(A1)]. \mforall{}[tr2:Id
{}\mrightarrow{} A2
{}\mrightarrow{} S
{}\mrightarrow{} S].
\mforall{}[X2:EClass(A2)]. \mforall{}[tr3:Id {}\mrightarrow{} A3 {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X3:EClass(A3)].
(State3(init;tr1;X1;tr2;X2;tr3;X3) = state-class3(init;tr1;X1;tr2;X2;tr3;X3))
Date html generated:
2015_07_22-PM-00_26_35
Last ObjectModification:
2015_02_04-PM-04_38_43
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