[Merged by Bors] - port: Algebra.Order.Monoid.NatCast #893
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Ruben-VandeVelde
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Ported by hand from current mathlib: 07fee0ca54c320250c98bacf31ca5f288b2bcbe2 This is thoroughly ridiculous, but it my fault for merging leanprover-community/mathlib#17820, see discussion on [zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/OfNat). Rather than proving 1 + 1 = 2 (I feel ridiculous), these lemmas should just happen later in mathlib, with stronger typeclasses. But these files are holding up the port, so its better to get this ported as is, and we can make it more sensible later... Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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Regenerated from the [port status wiki page](https://github.com/leanprover-community/mathlib/wiki/mathlib4-port-status). Relates to the following PRs: * `algebra.euclidean_domain.defs`: leanprover-community/mathlib4#871 * `algebra.group.ext`: leanprover-community/mathlib4#850 * `algebra.group_power.basic`: leanprover-community/mathlib4#874 * `algebra.hom.equiv.units.basic`: leanprover-community/mathlib4#895 * `algebra.hom.equiv.units.group_with_zero`: leanprover-community/mathlib4#901 * `algebra.order.group.instances`: leanprover-community/mathlib4#890 * `algebra.order.group.order_iso`: leanprover-community/mathlib4#895 * `algebra.order.group.units`: leanprover-community/mathlib4#898 * `algebra.order.monoid.nat_cast`: leanprover-community/mathlib4#893 * `algebra.order.monoid.type_tags`: leanprover-community/mathlib4#873 * `algebra.order.monoid.units`: leanprover-community/mathlib4#873 * `algebra.order.zero_le_one`: leanprover-community/mathlib4#893 * `combinatorics.quiver.push`: leanprover-community/mathlib4#868 * `control.traversable.basic`: leanprover-community/mathlib4#788 * `data.sum.order`: leanprover-community/mathlib4#880 * `group_theory.group_action.option`: leanprover-community/mathlib4#884 * `group_theory.group_action.sigma`: leanprover-community/mathlib4#885 * `group_theory.group_action.sum`: leanprover-community/mathlib4#882 * `group_theory.group_action.units`: leanprover-community/mathlib4#878 * `order.antisymmetrization`: leanprover-community/mathlib4#876
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Ported by hand from current mathlib: 07fee0ca54c320250c98bacf31ca5f288b2bcbe2
This is thoroughly ridiculous, but it my fault for merging leanprover-community/mathlib#17820, see discussion on zulip.
Rather than proving 1 + 1 = 2 (I feel ridiculous), these lemmas should just happen later in mathlib, with stronger typeclasses. But these files are holding up the port, so its better to get this ported as is, and we can make it more sensible later...