let D, E be non empty set ; :: thesis: for d being Element of D

for i being natural Number

for h being Function of D,E

for T being Tuple of i,D

for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let d be Element of D; :: thesis: for i being natural Number

for h being Function of D,E

for T being Tuple of i,D

for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let i be natural Number ; :: thesis: for h being Function of D,E

for T being Tuple of i,D

for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let h be Function of D,E; :: thesis: for T being Tuple of i,D

for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let T be Tuple of i,D; :: thesis: for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let F be BinOp of D; :: thesis: for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let H be BinOp of E; :: thesis: ( ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) implies h * (F [;] (d,T)) = H [;] ((h . d),(h * T)) )

assume A1: for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ; :: thesis: h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

for i being natural Number

for h being Function of D,E

for T being Tuple of i,D

for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let d be Element of D; :: thesis: for i being natural Number

for h being Function of D,E

for T being Tuple of i,D

for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let i be natural Number ; :: thesis: for h being Function of D,E

for T being Tuple of i,D

for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let h be Function of D,E; :: thesis: for T being Tuple of i,D

for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let T be Tuple of i,D; :: thesis: for F being BinOp of D

for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let F be BinOp of D; :: thesis: for H being BinOp of E st ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds

h * (F [;] (d,T)) = H [;] ((h . d),(h * T))

let H be BinOp of E; :: thesis: ( ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) implies h * (F [;] (d,T)) = H [;] ((h . d),(h * T)) )

assume A1: for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ; :: thesis: h * (F [;] (d,T)) = H [;] ((h . d),(h * T))