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Theorems · Theorem · order theory

Set.Nonempty.of_image2_left

∀ {α : Type u_1} {β : Type u_3} {γ : Type u_5} {f : α → β → γ} {s : Set α} {t : Set β},
  (Set.image2 f s t).Nonempty → s.Nonempty
Defined in
Mathlib.Data.Set.NAry
Cited by
12 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.add_eq_zero_iff · cited by 3Set.add_eq_zero_iffSet.mul_eq_one_iff · cited by 2Set.mul_eq_one_iffSet.Nonempty.of_infs_left · cited by 0Nonempty.of_infs_leftSet.Nonempty.of_mul_left · cited by 0Nonempty.of_mul_leftSet.Nonempty.of_sdiv_left · cited by 0Nonempty.of_sdiv_leftSet.Nonempty.of_smul_left · cited by 0Nonempty.of_smul_leftSet.Nonempty.of_sub_left · cited by 0Nonempty.of_sub_leftSet.Nonempty.of_sups_left · cited by 0Nonempty.of_sups_leftSet.Nonempty.of_vadd_left · cited by 0Nonempty.of_vadd_leftSet.Nonempty.of_vsub_left · cited by 0Nonempty.of_vsub_leftSet.Nonempty.of_add_left · cited by 0Nonempty.of_add_leftSet.Nonempty.of_div_left · cited by 0Nonempty.of_div_leftSet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.image2 · cited by 311Set.image2Set.image2_nonempty_iff · cited by 14Set.image2_nonempty_iffNonempty.of_image2_leftCITED BYCITES

Cites4

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Cited by12

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