Mathlib Map

Theorems · Theorem · order theory

Sublattice.ext

∀ {α : Type u_2} [inst : Lattice α] {L M : Sublattice α}, (∀ (a : α), a ∈ L ↔ a ∈ M) → L = M

Two sublattices are equal if they have the same elements.

Defined in
Mathlib.Order.Sublattice
Cited by
5 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Quot.sound
Assumes
Lattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Sublattice.pi_bot · cited by 1Sublattice.pi_botSublattice.top_prod · cited by 1Sublattice.top_prodSublattice.pi_top · cited by 0Sublattice.pi_topSublattice.pi_empty · cited by 0Sublattice.pi_emptySublattice.prod_top · cited by 0Sublattice.prod_topLattice · cited by 916LatticeSublattice · cited by 225SublatticeSetLike.ext · cited by 92SetLike.extSublattice.extCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.