Mathlib v3 is deprecated. Go to Mathlib v4

Commit 2022-06-03 22:33 00982865

View on Github →

feat(set_theory/ordinal/natural_ops): define natural addition (#14291) We define the natural addition operation on ordinals. We prove the basic properties, like commutativity, associativity, and cancellativity. We also provide the type synonym nat_ordinal for ordinals with natural operations, which allows us to take full advantage of this rich algebraic structure.

Estimated changes

added theorem nat_ordinal.induction
added theorem nat_ordinal.lt_wf
added theorem nat_ordinal.succ_def
added def nat_ordinal
added theorem ordinal.add_le_nadd
added theorem ordinal.lt_nadd_iff
added theorem ordinal.nadd_assoc
added theorem ordinal.nadd_comm
added theorem ordinal.nadd_def
added theorem ordinal.nadd_le_iff
added theorem ordinal.nadd_nat
added theorem ordinal.nadd_one
added theorem ordinal.nadd_succ
added theorem ordinal.nadd_zero
added theorem ordinal.nat_nadd
added theorem ordinal.one_nadd
added theorem ordinal.succ_nadd
added theorem ordinal.zero_nadd