Documentation

CombinatorialGames.OfSets

class OfSets (α : Type (u + 1)) (Valid : outParam ((Player → Set α) → Prop)) :
Type (u + 1)

Type class for the ofSets operation. Used to implement the !{st} and !{s | t} syntax.

  • ofSets (st : Player → Set α) (h : Valid st) [Small.{u, u + 1} ↑(st Player.left)] [Small.{u, u + 1} ↑(st Player.right)] : α

    Construct a combinatorial game from its Left and Right option sets.

    Conventions for notations in identifiers:

    • The recommended spelling of !{st}'h in identifiers is ofSets.

    • The recommended spelling of !{s | t}'h in identifiers is ofSets.

    • The recommended spelling of !{st} in identifiers is ofSets.

    • The recommended spelling of !{s | t} in identifiers is ofSets.

Instances

    Construct a combinatorial game from its Left and Right option sets.

    Conventions for notations in identifiers:

    • The recommended spelling of !{st}'h in identifiers is ofSets.
    Equations
    • One or more equations did not get rendered due to their size.
    Instances For

      Construct a combinatorial game from its Left and Right option sets.

      Conventions for notations in identifiers:

      • The recommended spelling of !{s | t}'h in identifiers is ofSets.
      Equations
      • One or more equations did not get rendered due to their size.
      Instances For

        Construct a combinatorial game from its Left and Right option sets.

        Conventions for notations in identifiers:

        • The recommended spelling of !{st} in identifiers is ofSets.
        Equations
        • One or more equations did not get rendered due to their size.
        Instances For

          Construct a combinatorial game from its Left and Right option sets.

          Conventions for notations in identifiers:

          • The recommended spelling of !{s | t} in identifiers is ofSets.
          Equations
          • One or more equations did not get rendered due to their size.
          Instances For
            Equations
            • One or more equations did not get rendered due to their size.
            Instances For
              theorem ofSets_eq_ofSets_cases {α : Type (u_1 + 1)} {Valid : (Player → Set α) → Prop} [OfSets α Valid] (st : Player → Set α) (h : Valid st) [Small.{u_1, u_1 + 1} ↑(st Player.left)] [Small.{u_1, u_1 + 1} ↑(st Player.right)] :
              !{st} = !{st Player.left | st Player.right}