Theorems · Theorem · order theory
WithBot.add_lt_add_left
∀ {α : Type u} [inst : Add α] {x y z : WithBot α} [inst_1 : LT α] [AddLeftStrictMono α], x ≠ ⊥ → y < z → x + y < x + z- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- AddLTAddLeftStrictMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement and proof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- WithBot.someproof · cited by 541
- AddLeftStrictMonostatement and proof · cited by 203
- WithBot.recBotCoeproof · cited by 101
- add_lt_add_rightproof · cited by 50
- WithBot.add_botproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- WithBot.add_lt_add_iff_leftproof · cited by 3
- WithBot.add_lt_add_of_le_of_ltproof · cited by 0