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Theorems · Theorem · order theory

Set.Nonempty.image2

∀ {α : Type u_1} {β : Type u_3} {γ : Type u_5} {f : α → β → γ} {s : Set α} {t : Set β},
  s.Nonempty → t.Nonempty → (Set.image2 f s t).Nonempty
Defined in
Mathlib.Data.Set.NAry
Cited by
14 results in Mathlib
Foundations
Depth 6 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.image2_nonempty_iff · cited by 14Set.image2_nonempty_iffcsInf_image2_eq_csInf_csInf · cited by 5csInf_image2_eq_csInf_csI…csSup_image2_eq_csSup_csSup · cited by 5csSup_image2_eq_csSup_csS…Set.Nonempty.add · cited by 3Nonempty.addSet.Nonempty.mul · cited by 3Nonempty.mulSet.Nonempty.vadd · cited by 2Nonempty.vaddnonempty_omegaLimit_of_isCompact_absorbing · cited by 1nonempty_omegaLimit_of_is…Set.Nonempty.smul · cited by 1Nonempty.smulSet.Nonempty.sdiv · cited by 0Nonempty.sdivSet.Nonempty.infs · cited by 0Nonempty.infsSet.Nonempty.sub · cited by 0Nonempty.subSet.Nonempty.div · cited by 0Nonempty.divSet.Nonempty.sups · cited by 0Nonempty.supsSet.Nonempty.vsub · cited by 0Nonempty.vsubSet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.image2 · cited by 311Set.image2Set.mem_image2_of_mem · cited by 40Set.mem_image2_of_memNonempty.image2CITED BYCITES

Cites4

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Cited by14

Results whose statement or proof uses this declaration.