proposition 3.54 Preimages respect the set operations
open in the book ·
parts/02-mathematical-methods/01-logic-sets.tex:1358
· p. 32
Rests on
- depends_on definition 3.53 Preimage ¶
-
depends_on
definition 3.35
Union, intersection, difference
¶
- depends_on definition 3.8 Conjunction ¶
- depends_on definition 3.9 Disjunction ¶
- depends_on definition 3.7 Negation ¶
- depends_on equation 3.47 eq:set-double-inclusion ¶
- proves proof ch:01-logic-sets@proof-8 ¶
Supports
Nothing declares a dependency on this node yet.
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Preimage | declared | parts/02-mathematical-methods/01-logic-sets.tex:1371 |
depends_on |
→ | Union, intersection, difference | declared | parts/02-mathematical-methods/01-logic-sets.tex:1371 |
depends_on |
→ | eq:set-double-inclusion | declared | parts/02-mathematical-methods/01-logic-sets.tex:1371 |
proves |
← | ch:01-logic-sets@proof-8 | declared | parts/02-mathematical-methods/01-logic-sets.tex:1374 |