Theorems · Definition · number theory

QuadraticMap.IsometryEquiv.trans

{R : Type u_2} →
  {M₁ : Type u_5} →
    {M₂ : Type u_6} →
      {M₃ : Type u_7} →
        {N : Type u_9} →
          [inst : CommSemiring R] →
            [inst_1 : AddCommMonoid M₁] →
              [inst_2 : AddCommMonoid M₂] →
                [inst_3 : AddCommMonoid M₃] →
                  [inst_4 : AddCommMonoid N] →
                    [inst_5 : Module R M₁] →
                      [inst_6 : Module R M₂] →
                        [inst_7 : Module R M₃] →
                          [inst_8 : Module R N] →
                            {Q₁ : QuadraticMap R M₁ N} →
                              {Q₂ : QuadraticMap R M₂ N} →
                                {Q₃ : QuadraticMap R M₃ N} →
                                  Q₁.IsometryEquiv Q₂ → Q₂.IsometryEquiv Q₃ → Q₁.IsometryEquiv Q₃

The composition of two isometric equivalences between quadratic forms.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv

Cited by

7 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule