thm1 : [16] -> Bit
property thm1 x = (x <<< 16 == x) && (x >>> 16 == x)

thm2 : [16] -> [16] -> Bit
property thm2 x i = x >>> i == x >>> (i && 0x000f)

thm3 : [15] -> [8] -> Bit
property thm3 x i = x <<< i == x <<< (i % 15)

thm4 : [15] -> [15] -> Bit
property thm4 x i = x <<< i >>> i == x

thm5 : [15] -> [3] -> Bit
property thm5 x i = x <<< i >>> i == x

thm6 : [8] -> [4] -> [4] -> Bit
property thm6 x i j = x <<< i >>> j == x <<< (i - j)