Theorems · Theorem · order theory
lt_add_iff_lt_left_or_exists_lt
∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α} [inst_1 : Add α] [CanonicallyOrderedAdd α] [AddLeftReflectLT α]
[IsLeftCancelAdd α], a < b + c ↔ a < b ∨ ∃ d < c, a = b + d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- LT.lt.trans_leproof · cited by 678
- CanonicallyOrderedAddstatement and proof · cited by 229
- lt_or_geproof · cited by 182
- IsLeftCancelAddstatement and proof · cited by 72
- le_self_addproof · cited by 68
- ExistsAddOfLE.exists_add_of_leproof · cited by 42
- AddLeftReflectLTstatement and proof · cited by 33
Cited by1
Results whose statement or proof uses this declaration.
- lt_add_iff_lt_right_or_exists_ltproof · cited by 0