Theorems · Theorem · general topology
IsPathConnected.neg
∀ {G : Type u_4} [inst : InvolutiveNeg G] [inst_1 : TopologicalSpace G] [ContinuousNeg G] {s : Set G},
IsPathConnected s → IsPathConnected (-s)- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- neg_negproof · cited by 960
- Set.negstatement · cited by 168
- InvolutiveNegstatement and proof · cited by 151
- ContinuousNegstatement and proof · cited by 119
- IsPathConnectedstatement and proof · cited by 65
- Set.image_neg_eq_negproof · cited by 52
- JoinedInproof · cited by 40
- ContinuousNeg.continuous_negproof · cited by 37
- Set.mem_negproof · cited by 23
- Set.neg_mem_negproof · cited by 10
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