let R be Field; :: thesis: for S being FieldExtension of R
for T being Subset of S
for a, b being Element of S
for x, y being Element of (FAdj (R,T)) st a = x & b = y holds
a * b = x * y
let S be FieldExtension of R; :: thesis: for T being Subset of S
for a, b being Element of S
for x, y being Element of (FAdj (R,T)) st a = x & b = y holds
a * b = x * y
let T be Subset of S; :: thesis: for a, b being Element of S
for x, y being Element of (FAdj (R,T)) st a = x & b = y holds
a * b = x * y
let a, b be Element of S; :: thesis: for x, y being Element of (FAdj (R,T)) st a = x & b = y holds
a * b = x * y
let x, y be Element of (FAdj (R,T)); :: thesis: ( a = x & b = y implies a * b = x * y )
assume A1: ( a = x & b = y ) ; :: thesis: a * b = x * y
the carrier of (FAdj (R,T)) = carrierFA T by dFA;
hence a * b = ( the multF of S || (carrierFA T)) . (x,y) by A1, RING_3:1
.= x * y by dFA ;
:: thesis: verum