Definition·D075
Concatenation of finite sequences
Join two finite sequences end to end: the second sequence's entries continue where the first's left off.
For
a set and
with
, define
with
from D074.
In words
For finite sequences f, g from A, with f of length m, their concatenation f‸g is f's entries in place, then g's entries renumbered to continue right after.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).
Remarks
The set
exists by Replacement applied to
; the union then exists by D004. That
, with the expected length and entries, is verified in T29.