Theorems · Theorem · order theory
AddQuantale.add_bot
∀ {α : Type u_3} [inst : AddSemigroup α] [inst_1 : CompleteLattice α] [IsAddQuantale α] {x : α}, x + ⊥ = ⊥- Defined in
- Mathlib.Algebra.Order.Quantale
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
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Cites12
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
- iSupproof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- iSup_congr_Propproof · cited by 247
- AddSemigroupstatement and proof · cited by 136
- iSup_negproof · cited by 49
- Set.mem_empty_iff_falseproof · cited by 32
- iSup_botproof · cited by 29
- sSup_emptyproof · cited by 19
- IsAddQuantalestatement and proof · cited by 13
- add_sSup_distribproof · cited by 4
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