let m be FinSequence of NAT ; :: thesis: for i being Nat st i = 3 & i in dom m holds
(IDEAoperationC m) . i = m . 2
let i be Nat; :: thesis: ( i = 3 & i in dom m implies (IDEAoperationC m) . i = m . 2 )
assume that
A1: i = 3 and
A2: i in dom m ; :: thesis: (IDEAoperationC m) . i = m . 2
(IDEAoperationC m) . i = IFEQ (i,2,(m . 3),(IFEQ (i,3,(m . 2),(m . i)))) by A2, Def13
.= IFEQ (i,3,(m . 2),(m . i)) by A1, FUNCOP_1:def 8
.= m . 2 by A1, FUNCOP_1:def 8 ;
hence (IDEAoperationC m) . i = m . 2 ; :: thesis: verum