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

A complete proof

1) First eliminations : a5=1%col, g2=4%block, c3=8%col, g3=6%block, c5=7%block lead to 27 filled cells.

2) Now :
Look at only possibles g5=8,i5=8 in their block. They forbid{d5=8, f5=8, e5=8}.
Now easy fillings up to 31 filled cells. (If needed, d6=8%col, e6=2%row, e5=4%col, d8=2%block)

3)
Look at only possibles c1=3,c7=3 in their col. Whether c7=3 (in which case c1=6%col) or c1=3, in both cases, we have no more {c1=4}.
Look at only possibles f6=1,h6=1 in their row. Whether h6=1 (in which case g7=1%col) or f6=1, in both cases, we have no more {f7=1}.
Look at only possibles a3=2,b3=2 in their row. Whether b3=2 (in which case a3=5%row) or a3=2, in both cases, we have no more {a3=9}.
Now easy fillings up to 81 filled cells. (If needed, a1=4%row, a2=9%col, a7=6%col, c1=6%col, e2=6%row, b2=3%cell, c7=3%block, f2=8%block, i2=7%row, e3=7%row, f4=7%row, a9=7%row, a3=2%col, b3=5%row, a8=5%col, c8=4%cell, b7=2%cell, h7=4%block, c6=5%cell, b6=4%row, f6=1%col, h6=9%cell, g7=9%col, f5=9%col, b4=9%col, i8=1%cell, e8=9%cell, h8=7%cell, e7=1%row, e9=8%block, f9=3%row, i9=5%row, i7=8%cell, f7=5%row, g9=2%row, i5=2%row, g5=8%block, h5=5%row, g4=1%col, h3=1%col, d1=1%row, d3=9%block, i3=3%row, i1=9%block, b5=6%cell, d4=6%block, d5=3%cell, e4=5%cell, e1=3%block, h4=3%col)

Short hints for a proof

Colors on 1s eliminate f7=1

1) easy to 27 filled.
2) Looking at 8 in R5, eliminate some possibles, then easy to 31 filled.
3) Looking at 16 in c1c7, at 25 in a3b3, eliminate some possibles; looking at 1 in R6, eliminate f7=1 then easy to unique solution.

Forbidding-chain-like proof

Colors on 1s eliminate f7=1

around 27 filled
(g5=8)==(i5=8) forbids {f5=8, e5=8, d5=8}
around 31 filled
(c1=3)==(c7=3)--(c7=6)==(c1=6) forbids {c1=4}
(f6=1)==(h6=1)--(g4=1)==(g7=1) forbids {f7=1}
(a3=2)==(b3=2)--(b3=5)==(a3=5) forbids {a3=9}