let n, m be Nat; for D being non empty set
for M1, M2 being Matrix of n,m,D holds Indices M1 = Indices M2
let D be non empty set ; for M1, M2 being Matrix of n,m,D holds Indices M1 = Indices M2
let M1, M2 be Matrix of n,m,D; Indices M1 = Indices M2
A1:
len M1 = n
by Def2;
A2:
len M2 = n
by Def2;
dom M1 = Seg n
by A1, FINSEQ_1:def 3;
hence
Indices M1 = Indices M2
by A2, A3, FINSEQ_1:def 3; verum