let K be Field; :: thesis: for T being K -monomorphic comRing
for f being Monomorphism of K,T
for a, b being Element of (embField f)
for a1, b1 being Element of K st a1 = a & b1 = b holds
( a * b = a1 * b1 & b * a = b1 * a1 )
let T be K -monomorphic comRing; :: thesis: for f being Monomorphism of K,T
for a, b being Element of (embField f)
for a1, b1 being Element of K st a1 = a & b1 = b holds
( a * b = a1 * b1 & b * a = b1 * a1 )
let f be Monomorphism of K,T; :: thesis: for a, b being Element of (embField f)
for a1, b1 being Element of K st a1 = a & b1 = b holds
( a * b = a1 * b1 & b * a = b1 * a1 )
let a, b be Element of (embField f); :: thesis: for a1, b1 being Element of K st a1 = a & b1 = b holds
( a * b = a1 * b1 & b * a = b1 * a1 )
let a1, b1 be Element of K; :: thesis: ( a1 = a & b1 = b implies ( a * b = a1 * b1 & b * a = b1 * a1 ) )
assume B1: ( a1 = a & b1 = b ) ; :: thesis: ( a * b = a1 * b1 & b * a = b1 * a1 )
reconsider ac = a, bc = b as Element of carr f by defemb;
thus a * b = (multemb f) . (a,b) by defemb
.= multemb (f,ac,bc) by defmult
.= a1 * b1 by B1, defmultf ; :: thesis: b * a = b1 * a1
thus b * a = (multemb f) . (b,a) by defemb
.= multemb (f,bc,ac) by defmult
.= b1 * a1 by B1, defmultf ; :: thesis: verum