let D be non empty set ; :: thesis: for d 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 commutative holds

F [;] (d,T) = F [:] (T,d)

let d 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 commutative holds

F [;] (d,T) = F [:] (T,d)

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

for F being BinOp of D st F is commutative holds

F [;] (d,T) = F [:] (T,d)

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

F [;] (d,T) = F [:] (T,d)

let F be BinOp of D; :: thesis: ( F is commutative implies F [;] (d,T) = F [:] (T,d) )

assume A1: F is commutative ; :: thesis: F [;] (d,T) = F [:] (T,d)

for i being natural Number

for T being Tuple of i,D

for F being BinOp of D st F is commutative holds

F [;] (d,T) = F [:] (T,d)

let d 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 commutative holds

F [;] (d,T) = F [:] (T,d)

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

for F being BinOp of D st F is commutative holds

F [;] (d,T) = F [:] (T,d)

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

F [;] (d,T) = F [:] (T,d)

let F be BinOp of D; :: thesis: ( F is commutative implies F [;] (d,T) = F [:] (T,d) )

assume A1: F is commutative ; :: thesis: F [;] (d,T) = F [:] (T,d)