Proof of X≤Y inverse to X˃Y

[Dieter]

The previous posts have shown (and proven) that repeating the same test command multiple times makes no sense at all: If the number of repetitions is even the result is always "true", so nothing is tested at all; two consecutive X≤Y? test are the same as a NOP. If the number of repetitions is odd the result is the same as a single test. So three times X≤Y? is the same as one X≤Y?.

But there is one exception: there are test commands that alter the test condition. The most relevant example is the FS?C test (or F2? and F3? on the HP67/97 that do the same). Here testing a flag also clears that flag. This means that the next FS?C test always tests false, and the original test is inverted.
So...

FS?C 00
FS?C 00

...is the same as FC?C 00

And on the HP67/97...

F2?
F2?

...is the same as FC?C 2.

Otherwise repeating the same test does not make any sense at all. As explained above.

Dieter