let D, E be non empty set ; :: thesis: for i being natural Number

for h being Function of D,E

for T1, T2 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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

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

for T1, T2 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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

let h be Function of D,E; :: thesis: for T1, T2 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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

let T1, T2 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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

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 .: (T1,T2)) = H .: ((h * T1),(h * T2)) )

assume A1: for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ; :: thesis: h * (F .: (T1,T2)) = H .: ((h * T1),(h * T2))

for h being Function of D,E

for T1, T2 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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

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

for T1, T2 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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

let h be Function of D,E; :: thesis: for T1, T2 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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

let T1, T2 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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

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 .: (T1,T2)) = H .: ((h * T1),(h * T2))

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 .: (T1,T2)) = H .: ((h * T1),(h * T2)) )

assume A1: for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ; :: thesis: h * (F .: (T1,T2)) = H .: ((h * T1),(h * T2))