Game

Mathlib.SetTheory.Game.Basic

URI: https://scilib.ai/kg/mathlib#SetTheory.Game

Lean4

/-- The type of combinatorial games. In ZFC, a combinatorial game is constructed from
  two sets of combinatorial games that have been constructed at an earlier
  stage. To do this in type theory, we say that a combinatorial pre-game is built
  inductively from two families of combinatorial games indexed over any type
  in Type u. The resulting type `PGame.{u}` lives in `Type (u+1)`,
  reflecting that it is a proper class in ZFC.
  A combinatorial game is then constructed by quotienting by the equivalence
  `x ≈ y ↔ x ≤ y ∧ y ≤ x`. -/
abbrev Game :=
  Quotient PGame.setoid

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Вычислительный центр им. А. А. Дороницына при ФИЦ «Информатика и Управление» РАН frccsc.ru