Theorems · Theorem · order theory

le_add_iff_lt_right_or_exists_le

∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α} [inst_1 : AddCommMagma α] [CanonicallyOrderedAdd α] [AddLeftMono α]
  [IsLeftCancelAdd α], a ≤ b + c ↔ a < c ∨ ∃ d ≤ b, a = d + c

Defined in: Mathlib.Algebra.Order.Monoid.Canonical.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder AddCommMagma CanonicallyOrderedAdd AddLeftMono IsLeftCancelAdd

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LinearOrderstatement and proof · cited by 8,572
add_commproof · cited by 1,535
AddLeftMonostatement and proof · cited by 687
CanonicallyOrderedAddstatement and proof · cited by 229
IsLeftCancelAddstatement and proof · cited by 72
AddCommMagmastatement and proof · cited by 32
le_add_iff_lt_left_or_exists_leproof · cited by 1

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