Theorems · Definition · order theory
RelSeries.smash
{α : Type u_1} → {r : SetRel α α} → (p q : RelSeries r) → p.last = q.head → RelSeries rGiven two series of the form a₀ -r→ ... -r→ X and X -r→ b > ...,
then a₀ -r→ ... -r→ X -r→ b ... is another series obtained by combining the given two.
- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetRelstatement and proof · cited by 581
- RelSeries.lengthproof · cited by 195
- RelSeriesstatement and proof · cited by 129
- RelSeries.laststatement and proof · cited by 114
- RelSeries.toFunproof · cited by 114
- RelSeries.headstatement and proof · cited by 89
Cited by15
Results whose statement or proof uses this declaration.
- Module.length_eq_add_of_exactproof · cited by 6
- RelSeries.smash_lengthstatement and proof · cited by 5
- RelSeries.last_smashstatement · cited by 4
- RelSeries.smash_castLEstatement · cited by 3
- Order.height_eq_index_of_length_eq_height_lastproof · cited by 2
- RelSeries.head_smashstatement · cited by 1
- RelSeries.smash_castAddstatement · cited by 1
- RelSeries.smash_natAddstatement · cited by 1
- RelSeries.smash_succ_castAddstatement · cited by 1
- RelSeries.smash_succ_natAddstatement · cited by 1
- Ideal.height_eq_height_add_of_liesOver_of_hasGoingDownproof · cited by 1
- LTSeries.exists_relSeries_covByproof · cited by 1