let D be non empty set ; :: thesis: for d1, d2 being Element of D

for i being natural Number

for T being Tuple of i,D

for F being BinOp of D st F is associative holds

F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

let d1, d2 be Element of D; :: thesis: for i being natural Number

for T being Tuple of i,D

for F being BinOp of D st F is associative holds

F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

let i be natural Number ; :: thesis: for T being Tuple of i,D

for F being BinOp of D st F is associative holds

F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

let T be Tuple of i,D; :: thesis: for F being BinOp of D st F is associative holds

F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

let F be BinOp of D; :: thesis: ( F is associative implies F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T))) )

assume A1: F is associative ; :: thesis: F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

for i being natural Number

for T being Tuple of i,D

for F being BinOp of D st F is associative holds

F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

let d1, d2 be Element of D; :: thesis: for i being natural Number

for T being Tuple of i,D

for F being BinOp of D st F is associative holds

F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

let i be natural Number ; :: thesis: for T being Tuple of i,D

for F being BinOp of D st F is associative holds

F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

let T be Tuple of i,D; :: thesis: for F being BinOp of D st F is associative holds

F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))

let F be BinOp of D; :: thesis: ( F is associative implies F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T))) )

assume A1: F is associative ; :: thesis: F [;] ((F . (d1,d2)),T) = F [;] (d1,(F [;] (d2,T)))