Theorems · Theorem · commutative algebra
MvPowerSeries.aeval.congr_simp
∀ {σ : Type u_1} {R : Type u_2} [inst : CommRing R] [inst_1 : UniformSpace R] {S : Type u_3} [inst_2 : CommRing S]
[inst_3 : UniformSpace S] {a a_1 : σ → S} (e_a : a = a_1) [inst_4 : IsTopologicalSemiring R]
[inst_5 : IsUniformAddGroup R] [inst_6 : IsUniformAddGroup S] [inst_7 : CompleteSpace S] [inst_8 : T2Space S]
[inst_9 : IsTopologicalRing S] [inst_10 : IsLinearTopology S S] [inst_11 : Algebra R S] [inst_12 : ContinuousSMul R S]
(ha : MvPowerSeries.HasEval a), MvPowerSeries.aeval ha = MvPowerSeries.aeval ⋯- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- AlgHomstatement · cited by 3,236
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- T2Spacestatement and proof · cited by 1,351
- ContinuousSMulstatement and proof · cited by 1,016
- MvPowerSeriesstatement · cited by 659
- IsTopologicalSemiringstatement and proof · cited by 442
- IsTopologicalRingstatement and proof · cited by 402
- IsUniformAddGroupstatement and proof · cited by 342
- IsLinearTopologystatement and proof · cited by 83
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.eval₂_substproof · cited by 0