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Diff — Subset

Revision #2376 → #3025 · back to history

modifiedProper subset1b5d0d5297f7
FieldFrom #2376To #3025
noteSet's `⊂` (HasSSubset, characterized by ssubset_def) is proper subset: `s ⊆ t ∧ ¬t ⊆ s`.Set.ssubset_def characterizes `s ⊂ t` as `s ⊆ t ∧ ¬t ⊆ s`, the proper-subset relation.
modified⊂ / ⊃ as proper subset / superset35caef8f3347
FieldFrom #2376To #3025
mathlib.declSet.instHasSSubsetSet.ssubset_def
noteMathlib follows this convention: `⊂` (Set.instHasSSubset) denotes proper subset, defined as `<`.Mathlib follows this convention: on `Set α`, `⊂` denotes proper subset (Set.ssubset_def unfolds it to `s ⊆ t ∧ ¬t ⊆ s`).
modifiedInclusion is the canonical partial orderd6f9505906f3
FieldFrom #2376To #3025
mathlib.declSet.instBooleanAlgebraSet.le_eq_subset
mathlib.match_kindgeneralizationexact
mathlib.moduleMathlib.Order.BooleanAlgebra.SetMathlib.Data.Set.Basic
noteThe canonical `≤` on `Set α` is inclusion (Set.le_eq_subset), provided by its BooleanAlgebra/partial-order structure.Set.le_eq_subset proves the canonical `≤` on `Set α` is exactly `⊆`.