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Theorems · Theorem · order theory

exists_le_add_iff_le_right

∀ {α : Type u_1} [inst : LinearOrder α] {P : α → Prop} {b c : α} [inst_1 : AddCommMagma α] [CanonicallyOrderedAdd α]
  [AddLeftMono α] [IsLeftCancelAdd α], (∃ a ≤ b + c, P a) ↔ (∃ a < c, P a) ∨ ∃ d ≤ b, P (d + c)
Defined in
Mathlib.Algebra.Order.Monoid.Canonical.Basic
Cited by
0 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderAddCommMagmaCanonicallyOrderedAddAddLeftMonoIsLeftCancelAdd
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LinearOrder · cited by 8572LinearOrderAddLeftMono · cited by 687AddLeftMonoCanonicallyOrderedAdd · cited by 229CanonicallyOrderedAddIsLeftCancelAdd · cited by 72IsLeftCancelAddAddCommMagma · cited by 32AddCommMagmaexists_le_add_iff_le_rightCITED BYCITES

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