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Theorems · Theorem · logic and foundations

ONote.repr_scale

∀ (x : ONote) [x.NF] (o : ONote) [o.NF], (x.scale o).repr = Ordinal.omega0 ^ x.repr * o.repr
Defined in
Mathlib.SetTheory.Ordinal.Notation
Cited by
4 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ONote.NFONote.NF
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ONote.split_dvd · cited by 2ONote.split_dvdONote.nf_repr_split · cited by 2ONote.nf_repr_splitONote.repr_opow_aux₂ · cited by 1ONote.repr_opow_aux₂ONote.repr_opow · cited by 1ONote.repr_opowmul_one · cited by 3885mul_oneadd_zero · cited by 2707add_zeroNat.cast_one · cited by 2501Nat.cast_oneOrdinal · cited by 1688OrdinalOrdinal.omega0 · cited by 197Ordinal.omega0ONote · cited by 88ONoteONote.repr · cited by 45ONote.reprONote.NF · cited by 36ONote.NFONote.scale · cited by 9ONote.scaleONote.repr_mul · cited by 4ONote.repr_mulONote.scale_eq_mul · cited by 1ONote.scale_eq_mulONote.repr_scaleCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.