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@keithprosser
If your computer is oriented { positioned } in specific way, the first "a" on left is not equal to the other one on right right, because, its lies on a differrent longitude.I can't think of anything that one can prove without relying on a=a -> true at some point.
If computer is turned 90 degrees, their equal, in that both are on same longitude, but no longer on same latitude.
By the way, if you havent yet figured this out, I'm presenting a chewing-gum mind-game. :---(