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Theorems · Theorem · order theory

le_add_of_forall_lt

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] [DenselyOrdered α] {a b c : α},
  (∀ a' > a, ∀ b' > b, c ≤ a' + b') → c ≤ a + b
Defined in
Mathlib.Algebra.Order.Group.DenselyOrdered
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupLinearOrderAddLeftMonoDenselyOrdered
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Around this declaration

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

liminf_add_le · cited by 0liminf_add_lelimsup_add_le · cited by 0limsup_add_leAddCommGroup · cited by 12871AddCommGroupLinearOrder · cited by 8572LinearOrderLE.le.trans · cited by 3151le.transLT.lt.le · cited by 2189lt.leAddLeftMono · cited by 687AddLeftMonoDenselyOrdered · cited by 471DenselyOrderedle_of_forall_gt_imp_ge_of_dense · cited by 21le_of_forall_gt_imp_ge_of…le_add_of_forall_ltCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.