proposition 3.63 prop:inf-equipotence-equivalence

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:1635 · p. 36

Rests on

depends_on definition 3.62 Equipotence ¶
- depends_on definition 3.47 Bijective map ¶
- depends_on definition 3.40 Cardinal ¶
depends_on definition 3.50 Identity map ¶
depends_on definition 3.51 Inverse map ¶
- depends_on definition 3.47 Bijective map ¶ ↺
- depends_on definition 3.49 Composition map ¶
- depends_on definition 3.50 Identity map ¶ ↺
depends_on proposition 3.57 Composition of bijective maps ¶
- depends_on definition 3.51 Inverse map ¶ ↺
- depends_on proposition 3.56 Composition is associative ¶
  - depends_on definition 3.49 Composition map ¶ ↺
  - depends_on definition 3.50 Identity map ¶ ↺
  - proves proof ch:01-logic-sets@proof-9 ¶
- depends_on proposition 3.48 Characterization of bijectivity ¶
  - depends_on definition 3.47 Bijective map ¶ ↺
  - depends_on definition 3.45 Injective map ¶
  - depends_on definition 3.46 Surjective map ¶
  - proves proof ch:01-logic-sets@proof-7 ¶
- proves proof ch:01-logic-sets@proof-10 ¶
proves proof ch:01-logic-sets@proof-12 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Equipotence	declared	parts/02-mathematical-methods/01-logic-sets.tex:1637
`depends_on`	→	Identity map	declared	parts/02-mathematical-methods/01-logic-sets.tex:1637
`depends_on`	→	Inverse map	declared	parts/02-mathematical-methods/01-logic-sets.tex:1637
`depends_on`	→	Composition of bijective maps	declared	parts/02-mathematical-methods/01-logic-sets.tex:1637
`proves`	←	ch:01-logic-sets@proof-12	declared	parts/02-mathematical-methods/01-logic-sets.tex:1640