instLattice — Mathlib

English

If α and β are lattices, then α × β is a lattice with coordinatewise operations: (a,b) ⊔ (c,d) = (a ⊔ c, b ⊔ d) and (a,b) ⊓ (c,d) = (a ⊓ c, b ⊓ d).

Русский

Если α и β — решётки, то α×β — решётка, коэффициентно задаваемая через ⊔ и ⊓: (a,b) ⊔ (c,d) = (a ⊔ c, b ⊔ d), (a,b) ⊓ (c,d) = (a ⊓ c, b ⊓ d).

LaTeX

$$$ (a,b) \lor (c,d) = (a \lor c, b \lor d) \quad\land\quad (a,b) \land (c,d) = (a \land c, b \land d) $$$

Lean4

instance instLattice [Lattice α] [Lattice β] : Lattice (α × β) where

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