Theorems · Theorem · order theory
Subtype.mk_eq_bot_iff
∀ {α : Type u} {p : α → Prop} [inst : PartialOrder α] [inst_1 : OrderBot α] [inst_2 : OrderBot (Subtype p)],
p ⊥ → ∀ {x : α} (hx : p x), ⟨x, hx⟩ = ⊥ ↔ x = ⊥- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- PartialOrderOrderBotOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- Subtype.coe_eq_bot_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- map_prime_of_factor_orderIsoproof · cited by 2
- Module.End.invtSubmodule.disjoint_mk_iffproof · cited by 0
- RootPairing.invtRootSubmodule.eq_bot_iffproof · cited by 0
- Module.End.invtSubmodule.mk_eq_bot_iffproof · cited by 0