theorem Th17:
  (i"/\"j) => k = i => (j => k)
proof
A1: (j"/\"i)"/\"((i"/\"j)=>k) = j"/\"(i "/\" ( ( i "/\"j)=>k)) by
LATTICES:def 7;
  (i"/\"j)"/\"((i"/\"j)=>k) [= k by FILTER_0:def 7;
  then i"/\"((i"/\"j)=>k) [= j=>k by A1,FILTER_0:def 7;
  then
A2: (i"/\"j)=>k [= i=>(j=>k) by FILTER_0:def 7;
A3: j"/\"(i"/\"(i=>(j=>k))) = j"/\"i"/\"(i=>(j=>k)) by LATTICES:def 7;
  i"/\"(i=>(j=>k)) [= j=>k by FILTER_0:def 7;
  then
A4: j"/\"(i"/\"(i=>(j=>k))) [= j"/\"(j=>k) by LATTICES:9;
  j"/\"(j=>k) [= k by FILTER_0:def 7;
  then i"/\"j"/\"(i=>(j=>k)) [= k by A4,A3,LATTICES:7;
  then i=>(j=>k) [= (i"/\"j)=>k by FILTER_0:def 7;
  hence thesis by A2,LATTICES:8;
end;
