i,x,y:Id, k:Knd, T,A,B:Type, f:(A
BTA).
Thm*
y = x
Thm*
Thm* @i: ma-single-effect1(x;A;y;B;k;T;f)
Dsys
Thm* & (
D:Dsys.
Thm* & (@i: ma-single-effect1(x;A;y;B;k;T;f)
D
Thm* & (
Thm* & (D
Thm* & (realizes es.(vartype(i;x)
r A) & (vartype(i;y) r B)
Thm* & (realizes es.& (
e:E.
Thm* & (realizes es.& (loc(e) = i
Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = k
Knd (valtype(e) r T))
Thm* & (realizes es.& (
e:E.
Thm* & (realizes es.& (loc(e) = i
Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = k
Knd
Thm* & (realizes es.& (
Thm* & (realizes es.& ((x after e) = f((x when e),(y when e),val(e))
A))i,x:Id, k:Knd, ds:a:Id fp-> Type, da:a:Knd fp-> Type,
Thm*
f:(State(ds)ma-valtype(da; k)ds(x)?Void).
Thm* @i: ma-single-effect(ds; da; k; x; f)
Dsys
Thm* & (
D:Dsys.
Thm* & (@i: ma-single-effect(ds; da; k; x; f)
D
Thm* & (
Thm* & (D
Thm* & (realizes es.(
x:Id. vartype(i;x) r ds(x)?Top)
Thm* & (realizes es.& (
e:E.
Thm* & (realizes es.& (loc(e) = i
Id
Thm* & (realizes es.& (
Thm* & (realizes es.& ((valtype(e)
r ma-valtype(da; kind(e))))
Thm* & (realizes es.& (
e:E.
Thm* & (realizes es.& (loc(e) = i
Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = k
Knd
Thm* & (realizes es.& (
Thm* & (realizes es.& ((x after e) = f((
z.(z when e)),val(e)) ds(x)?Top))eq:EqDecider(A), f,g:a:A fp-> Top, x:A, z:Top.
Thm* f
g(x)?z ~ if x dom(f)
f(x)?z else g(x)?z fieq:EqDecider(A), x,y:A, v:Top. x dom(y : v) 
x = y