06/02/03 tough puzzle from sudoku.com.au

Today's puzzle has the particularity to need only two eliminations to be solved.

Want to see the whole thing? A complete proof
Just stuck somewhere and willing to have still work to do ? Short hints for a proof
Studied enough forbidding chains to appreciate this Forbidding-chain-like proof ?

A complete proof

1) First eliminations : i5=2%row, h5=3%row, h4=9%col, i7=9%col, i9=8%block lead to 27 filled cells.

2) Now :
Look at only possibles d6=8,b6=8 in their row. Whether b6=8 (in which case d6=9%row) or d6=8, in both cases, we have no more {d6=5, d6=4, d6=1}.
Now easy fillings up to 43 filled cells. (If needed, f4=5%block, a4=8%row, b7=8%block, d6=8%row, h3=8%row, f2=8%block, f1=7%block, f5=9%col, d5=6%block, e3=3%block, e7=2%col, h1=4%cell, b6=9%col, c4=6%row, a8=2%block, i1=3%row)

3)
Look at only possibles i6=1,i2=1 in their col. Whether i6=1 (in which case g6=5%row) or i2=1 (in which case h2=7%row,h8=5%cell), in both cases, we have no more {g8=5, g7=5}.
Now easy fillings up to 81 filled cells. (If needed, a7=5%row, a9=6%block, d9=5%row, c9=7%row, d8=1%block, b9=1%row, b5=4%cell, e6=4%col, c6=1%cell, a5=7%cell, c7=4%block, g8=4%block, f9=4%col, e5=1%row, e4=7%cell, g6=7%col, g3=5%col, i3=6%row, f8=6%row, g7=6%row, g1=2%block, g4=1%col, h8=5%col, i8=7%cell, h2=7%row, f7=3%block, a1=1%row, a3=9%block, d1=9%block, i2=1%row, a2=4%cell, d3=4%block, b8=3%cell, b2=5%cell, c3=2%cell, c2=3%cell, i6=5%row, d2=2%cell)

Short hints for a proof

Second and last elimination needs nonagon


1) easy fillings to 27 filled.
2) eliminate d6=5 (hidden pair, 2 sets), then easy fillings to 43 filled.
3) eliminate g7=5 (which implies a contradiction in i2, 4 sets). Then easy fillings to the end.

Forbidding-chain-like proof

Second and last elimination needs nonagon


around 27 filled
(d6=8)==(b6=8)--(b6=9)==(d6=9) forbids {d6=1, d6=4, d6=5}
around 31 filled
(g6=5)==(i6=5)--(i6=1)==(i2=1)--(i2=7)==(h2=7)--(h8=7)==(h8=5) forbids {g8=5, g7=5}

That's all for today, folks...