Theorems · Theorem · algebraic topology
Bundle.Pretrivialization.mem_target
∀ {B : Type u_1} {F : Type u_2} {Z : Type u_4} [inst : TopologicalSpace B] [inst_1 : TopologicalSpace F] {proj : Z → B}
(e : Bundle.Pretrivialization F proj) {x : B × F}, x ∈ e.target ↔ x.1 ∈ e.baseSet- Cited by
- 8 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- PartialEquiv.targetstatement · cited by 650
- Set.mem_preimageproof · cited by 190
- Bundle.Pretrivializationstatement and proof · cited by 111
- Bundle.Pretrivialization.baseSetstatement and proof · cited by 80
- Bundle.Pretrivialization.toPartialEquivstatement · cited by 77
- Set.prod_univproof · cited by 14
- Bundle.Pretrivialization.target_eqproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- Bundle.Trivialization.mem_targetproof · cited by 7
- Bundle.Pretrivialization.proj_symm_apply'proof · cited by 7
- FiberPrebundle.isOpen_sourceproof · cited by 1
- Bundle.Pretrivialization.mk_mem_targetproof · cited by 1
- Bundle.Pretrivialization.apply_symm_apply'proof · cited by 1
- Bundle.Pretrivialization.proj_surjOn_baseSetproof · cited by 1
- Bundle.Trivialization.mk_mem_targetproof · cited by 0
- Bundle.Pretrivialization.preimage_symm_proj_baseSetproof · cited by 0