Theorems · Theorem · functional analysis
TrivSqZeroExt.exp_def_of_smul_comm
∀ {R : Type u_3} {M : Type u_4} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [inst_3 : Module Rᵐᵒᵖ M]
[inst_4 : SMulCommClass R Rᵐᵒᵖ M] [inst_5 : TopologicalSpace R] [inst_6 : TopologicalSpace M]
[inst_7 : IsTopologicalRing R] [inst_8 : IsTopologicalAddGroup M] [inst_9 : ContinuousSMul R M]
[inst_10 : ContinuousSMul Rᵐᵒᵖ M] [Algebra ℚ R] [Module ℚ M] [T2Space R] [T2Space M] (x : TrivSqZeroExt R M),
MulOpposite.op x.fst • x.snd = x.fst • x.snd →
NormedSpace.exp x = TrivSqZeroExt.inl (NormedSpace.exp x.fst) + TrivSqZeroExt.inr (NormedSpace.exp x.fst • x.snd)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- zero_addproof · cited by 2,366
- SummationFilter.unconditionalproof · cited by 2,068
- SMulCommClassstatement and proof · cited by 1,927
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- T2Spacestatement and proof · cited by 1,351
- tsumproof · cited by 1,148
Cited by3
Results whose statement or proof uses this declaration.
- TrivSqZeroExt.exp_inrproof · cited by 3
- TrivSqZeroExt.exp_defproof · cited by 2
- TrivSqZeroExt.exp_inlproof · cited by 0