Theorems · Theorem · general topology
Joined.mul
∀ {M : Type u_4} [inst : Mul M] [inst_1 : TopologicalSpace M] [ContinuousMul M] {a b c d : M},
Joined a b → Joined c d → Joined (a * c) (b * d)- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousMulstatement and proof · cited by 343
- Joinedstatement and proof · cited by 29
- Joined.somePathproof · cited by 12
- Path.mulproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Unitary.mem_pathComponentOne_iffproof · cited by 0
- Joined.listProdproof · cited by 0