       (i0 < &LENGTH ws <=> Num i0 < LENGTH ws)` by intLib.COOPER_TAC     \\ fs [] \\ imp_res_tac LIST_REL_LENGTH \\ fs []     \\ fs [option_case_eq] \\ rveq \\ fs [v_rel_def,Unit_def,EVAL ``tuple_tag``]     \\ fs [state_rel_def,store_rel_def,EL_LUPDATE]     \\ strip_tac     \\ first_x_assum (qspec_then `i` mp_tac)     \\ IF_CASES_TAC     \\ fs [FLOOKUP_UPDATE,EL_LUPDATE,EL_APPEND0,EL_APPEND0]     \\ 