let ins be Instruction of SCM+FSA ; :: thesis: ( InsCode ins = 10 implies ex a, b being Int-Location ex fa being FinSeq-Location st ins = fa,a := b )
assume A1:
InsCode ins = 10
; :: thesis: ex a, b being Int-Location ex fa being FinSeq-Location st ins = fa,a := b
A2:
( ins in SCM-Instr \/ { [L,<*dB,fA,dA*>] where L is Element of Segm 13, dB, dA is Element of SCM+FSA-Data-Loc , fA is Element of SCM+FSA-Data*-Loc : L in {9,10} } or ins in { [K,<*dC,fB*>] where K is Element of Segm 13, dC is Element of SCM+FSA-Data-Loc , fB is Element of SCM+FSA-Data*-Loc : K in {11,12} } )
by XBOOLE_0:def 3;
now assume
ins in { [K,<*dC,fB*>] where K is Element of Segm 13, dC is Element of SCM+FSA-Data-Loc , fB is Element of SCM+FSA-Data*-Loc : K in {11,12} }
;
:: thesis: contradictionthen consider K being
Element of
Segm 13,
dC being
Element of
SCM+FSA-Data-Loc ,
fB being
Element of
SCM+FSA-Data*-Loc such that A3:
ins = [K,<*dC,fB*>]
and A4:
K in {11,12}
;
(
K = 11 or
K = 12 )
by A4, TARSKI:def 2;
hence
contradiction
by A1, A3, MCART_1:7;
:: thesis: verum end;
then
( ins in SCM-Instr or ins in { [L,<*dB,fA,dA*>] where L is Element of Segm 13, dB, dA is Element of SCM+FSA-Data-Loc , fA is Element of SCM+FSA-Data*-Loc : L in {9,10} } )
by A2, XBOOLE_0:def 3;
then consider L being Element of Segm 13, dB, dA being Element of SCM+FSA-Data-Loc , fA being Element of SCM+FSA-Data*-Loc such that
A5:
ins = [L,<*dB,fA,dA*>]
and
L in {9,10}
by A1, AMI_5:36;
reconsider c = dB, b = dA as Int-Location by Def4;
reconsider f = fA as FinSeq-Location by Def5;
take
b
; :: thesis: ex b being Int-Location ex fa being FinSeq-Location st ins = fa,b := b
take
c
; :: thesis: ex fa being FinSeq-Location st ins = fa,b := c
take
f
; :: thesis: ins = f,b := c
thus
ins = f,b := c
by A1, A5, MCART_1:7; :: thesis: verum