Very Basic Chess Endings

I'm almost too embarrassed to discuss the diagrammed position, as it is one of the most fundamental ideas in Rook and Pawn Endings. But (a) I assume not everyone has seen it and (b) at least two games at the SIO ran on far longer than they should because it wasn't clear that the player with the pawn quite knew what they were doing.
The position is of course the "Lucena Position". White would like to get king out of the way of the pawn, allowing it to queen, but is met by annoying checks from the black rook. The simple plan is to (1) get the pawn to the 7th rank (2) drive the enemy king away from the e file with a rook check (3) move the rook to the 4th or 5th rank so that after (4) moving the king to f7 (5) enemy checks are met with a zig zag to g6 (or g5) when blacks last check on the g file is blocked by the white rook.
The actual moves to do this are 1.Kh7 Rh2+ 2.Kg8 Rg2 3.g7 Rh2 4.Re1+ Kd7 5.Re4 Rh1 6.Kf7 Rf1+ 7.Kg6 Rg1+ 8.Kf6 Rf1+ 9.Kg5 Rg1+ 10.Rg4 +- Of course 4. ... Kf6 is met by 5.Kf8 avoiding any more checks.
In the actual games at the SIO one player failed to transpose into the Lucena position, by giving up an extra pawn, and after much play (and muttering by the spectators), managed to only draw the game. In the other, the player with the extra pawn was on the verge of defeating his (unnamed) GM opponent, but made heavy weather of it, possibly due to the pressure of getting the win. I suspect his opponent sensed this, as at some point the (unnamed) GM stopped the clock and bizarrely claimed a draw by two-fold repetition. The arbiting team treated this as a claim for a three-fold repetition, which was then rejected as incorrect. The disturbance didn't effect the outcome of the game as the (unnamed) GM eventually lost.