let n be Nat; :: thesis: for D being non empty set
for M1 being Matrix of n,D
for i, j being Nat st [i,j] in Indices M1 holds
[j,i] in Indices M1
let D be non empty set ; :: thesis: for M1 being Matrix of n,D
for i, j being Nat st [i,j] in Indices M1 holds
[j,i] in Indices M1
let M1 be Matrix of n,D; :: thesis: for i, j being Nat st [i,j] in Indices M1 holds
[j,i] in Indices M1
let i, j be Nat; :: thesis: ( [i,j] in Indices M1 implies [j,i] in Indices M1 )
assume A1: [i,j] in Indices M1 ; :: thesis: [j,i] in Indices M1
A2: Indices M1 = [:(Seg n),(Seg n):] by Th25;
[i,j] in [:(Seg n),(Seg n):] by A1, Th25;
then ( j in Seg n & i in Seg n ) by ZFMISC_1:106;
hence [j,i] in Indices M1 by A2, ZFMISC_1:106; :: thesis: verum