let SBT be Permutation of (8 -tuples_on BOOLEAN); :: thesis: for m being Nat
for text being Element of 4 -tuples_on (4 -tuples_on (8 -tuples_on BOOLEAN)) holds ((InvSubBytes SBT) * InvShiftRows) . ((ShiftRows * (SubBytes SBT)) . text) = text
let m be Nat; :: thesis: for text being Element of 4 -tuples_on (4 -tuples_on (8 -tuples_on BOOLEAN)) holds ((InvSubBytes SBT) * InvShiftRows) . ((ShiftRows * (SubBytes SBT)) . text) = text
let text be Element of 4 -tuples_on (4 -tuples_on (8 -tuples_on BOOLEAN)); :: thesis: ((InvSubBytes SBT) * InvShiftRows) . ((ShiftRows * (SubBytes SBT)) . text) = text
thus ((InvSubBytes SBT) * InvShiftRows) . ((ShiftRows * (SubBytes SBT)) . text) = ((InvSubBytes SBT) * InvShiftRows) . (ShiftRows . ((SubBytes SBT) . text)) by FUNCT_2:15
.= (InvSubBytes SBT) . (InvShiftRows . (ShiftRows . ((SubBytes SBT) . text))) by FUNCT_2:15
.= (InvSubBytes SBT) . ((SubBytes SBT) . text) by INV04
.= text by INV07 ; :: thesis: verum