let X be non empty disjoint_with_NAT set ; :: thesis: for I1, I2 being Element of (FreeUnivAlgNSG ECIW-signature ,X) holds I1 \; I2 = 2 -tree I1,I2
set S = ECIW-signature ;
reconsider s = ECIW-signature as non empty FinSequence of omega ;
set A = FreeUnivAlgNSG ECIW-signature ,X;
let I1, I2 be Element of (FreeUnivAlgNSG ECIW-signature ,X); :: thesis: I1 \; I2 = 2 -tree I1,I2
A1: 2 in dom the charact of (FreeUnivAlgNSG ECIW-signature ,X) by Def11;
reconsider f = the charact of (FreeUnivAlgNSG ECIW-signature ,X) . 2 as non empty homogeneous quasi_total binary PartFunc of (the carrier of (FreeUnivAlgNSG ECIW-signature ,X) * ),the carrier of (FreeUnivAlgNSG ECIW-signature ,X) by Def11;
A2: f = FreeOpNSG 2,ECIW-signature ,X by A1, FREEALG:def 12;
A3: 2 in dom ECIW-signature by Th54;
then s /. 2 = ECIW-signature . 2 by PARTFUN1:def 8;
then A4: dom (FreeOpNSG 2,ECIW-signature ,X) = 2 -tuples_on (TS (DTConUA ECIW-signature ,X)) by A3, Th54, FREEALG:def 11;
A5: <*I1,I2*> in 2 -tuples_on (TS (DTConUA ECIW-signature ,X)) by FINSEQ_2:157;
thus I1 \; I2 = f . <*I1,I2*> by A1, FUNCT_7:def 1
.= (Sym 2,ECIW-signature ,X) -tree <*I1,I2*> by A2, A3, A4, A5, FREEALG:def 11
.= 2 -tree I1,I2 by A3, FREEALG:def 10 ; :: thesis: verum