Axiomatic WikiWWikiDDefinitionsSubset
Definition·D001
A is a subset of B when every member of A is a member of B.
In words
A is a subset of B exactly when for every x, if x belongs to A then x belongs to B.
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 · A09 (computed from the citation graph, not asserted).
Remarks
The subset relation, written
. Equality is mutual inclusion, so
, which is the content of A01 read both ways.
Used by
Propose an edit3 published revisions
- 7/11/2026 · Benjamin· Fix Mathlib link: add the #doc fragment doc-gen4's find endpoint requires (old link 404'd). Content unchanged.→what changed →
- 7/11/2026 · Benjamin· Backfill: add plain-English prose and Mathlib docs link→what changed →
- 7/11/2026 · Benjamin· Initial foundations seed→what changed →