:set prover-stats = off
transpose [0x0, 1 ...]
:pro (\(x:[4]) -> (transpose [x ...])@0@0 == False)

:pro (\(x:[4]) -> (transpose [x ...])@0@0 == x@0)
:pro (\(x:[4]) -> (transpose [x ...])@1@0 == x@1)
:pro (\(x:[4]) -> (transpose [x ...])@2@0 == x@2)
:pro (\(x:[4]) -> (transpose [x ...])@3@0 == x@3)

:pro (\(x:[4]) -> (transpose [x ...])@3@1 == ~(x@3))