fact stringlengths 6 14.3k | statement stringlengths 1 2.88k | proof stringlengths 0 13.9k | type stringclasses 12
values | symbolic_name stringlengths 0 131 | library stringclasses 417
values | filename stringlengths 17 80 | imports listlengths 0 16 | deps listlengths 0 64 | docstring stringlengths 8 10.2k ⌀ | line_start int64 6 4.24k | line_end int64 7 4.25k | has_proof bool 2
classes | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
hom_trivialization_at_target (x₀ : B) :
(trivialization_at (F₁ →SL[σ] F₂) (λ x, E₁ x →SL[σ] E₂ x) x₀).target =
((trivialization_at F₁ E₁ x₀).base_set ∩ (trivialization_at F₂ E₂ x₀).base_set) ×ˢ set.univ :=
rfl | hom_trivialization_at_target (x₀ : B) :
(trivialization_at (F₁ →SL[σ] F₂) (λ x, E₁ x →SL[σ] E₂ x) x₀).target =
((trivialization_at F₁ E₁ x₀).base_set ∩ (trivialization_at F₂ E₂ x₀).base_set) ×ˢ set.univ | rfl | lemma | hom_trivialization_at_target | topology.vector_bundle | src/topology/vector_bundle/hom.lean | [
"topology.vector_bundle.basic",
"analysis.normed_space.operator_norm"
] | [] | null | 337 | 341 | true | https://github.com/leanprover-community/mathlib | 65a1391a0106c9204fe45bc73a039f056558cb83 |
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