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[Merged by Bors] - feat(Data/Matrix/Basic): 0 ≤ 1 #12911

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[Merged by Bors] - feat(Data/Matrix/Basic): 0 ≤ 1 #12911

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feat(Data/Matrix/Basic): 0 ≤ 1
madvorak May 14, 2024
4de5930
Update Mathlib/Data/Matrix/Basic.lean
madvorak May 15, 2024
c35a835
cosmetic improvement
madvorak May 15, 2024
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8 changes: 8 additions & 0 deletions Mathlib/Data/Matrix/Basic.lean
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Expand Up @@ -567,6 +567,14 @@ theorem one_eq_pi_single {i j} : (1 : Matrix n n α) i j = Pi.single (f := fun _
simp only [one_apply, Pi.single_apply, eq_comm]
#align matrix.one_eq_pi_single Matrix.one_eq_pi_single

lemma zero_le_one_elem [Preorder α] [ZeroLEOneClass α] (i i' : n) :
0 ≤ (1 : Matrix n n α) i i' := by
by_cases hi : i = i' <;> simp [hi]

lemma zero_le_one_row [Preorder α] [ZeroLEOneClass α] (i : n) :
0 ≤ (1 : Matrix n n α) i :=
fun i' => zero_le_one_elem i i'
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end One

instance instAddMonoidWithOne [AddMonoidWithOne α] : AddMonoidWithOne (Matrix n n α) where
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