let n be Element of NAT ; :: thesis: for x, y being FinSequence
for p being set holds
( n -BitMajorityOutput x,y <> [p,'&' ] & n -BitMajorityOutput x,y <> [p,'xor' ] )
let x, y be FinSequence; :: thesis: for p being set holds
( n -BitMajorityOutput x,y <> [p,'&' ] & n -BitMajorityOutput x,y <> [p,'xor' ] )
let p be set ; :: thesis: ( n -BitMajorityOutput x,y <> [p,'&' ] & n -BitMajorityOutput x,y <> [p,'xor' ] )
A1: dom '&' = 2 -tuples_on BOOLEAN by FUNCT_2:def 1;
A2: dom 'xor' = 2 -tuples_on BOOLEAN by FUNCT_2:def 1;
A3: proj1 ([p,'&' ] `2 ) = 2 -tuples_on BOOLEAN by A1, MCART_1:7;
A4: proj1 ([p,'xor' ] `2 ) = 2 -tuples_on BOOLEAN by A2, MCART_1:7;
( proj1 ((n -BitMajorityOutput x,y) `2 ) = 0 -tuples_on BOOLEAN or proj1 ((n -BitMajorityOutput x,y) `2 ) = 3 -tuples_on BOOLEAN ) by Th25;
hence ( n -BitMajorityOutput x,y <> [p,'&' ] & n -BitMajorityOutput x,y <> [p,'xor' ] ) by A3, A4, FINSEQ_2:130; :: thesis: verum