let f, g be Function of I[01],R^1; :: thesis: ( ( for x being Point of I[01] holds f . x = r * x ) & ( for x being Point of I[01] holds g . x = r * x ) implies f = g )

assume that

A2: for x being Point of I[01] holds f . x = r * x and

A3: for x being Point of I[01] holds g . x = r * x ; :: thesis: f = g

for x being Point of I[01] holds f . x = g . x

assume that

A2: for x being Point of I[01] holds f . x = r * x and

A3: for x being Point of I[01] holds g . x = r * x ; :: thesis: f = g

for x being Point of I[01] holds f . x = g . x

proof

hence
f = g
; :: thesis: verum
let x be Point of I[01]; :: thesis: f . x = g . x

thus f . x = r * x by A2

.= g . x by A3 ; :: thesis: verum

end;thus f . x = r * x by A2

.= g . x by A3 ; :: thesis: verum