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fpvandoornFloris van Doorn
andcommitted
fix(order/sub): make arguments explicit (#9541)
* This makes some arguments of lemmas explicit. * These lemmas were not used in places where the implicitness/explicitness of the arguments matters * Providing the arguments is sometimes useful, especially in `rw ← ...` * This follows the explicitness of similar lemmas (like the instantiations for `nat`). Co-authored-by: Floris van Doorn <fpv@andrew.cmu.edu>
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src/algebra/order/sub.lean

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@@ -245,11 +245,11 @@ lemma eq_sub_of_add_eq'' (h : a + c = b) : a = b - c :=
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contravariant.add_le_cancellable.eq_sub_of_add_eq h
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@[simp]
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lemma add_sub_cancel_right : a + b - b = a :=
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lemma add_sub_cancel_right (a b : α) : a + b - b = a :=
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contravariant.add_le_cancellable.add_sub_cancel_right
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@[simp]
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lemma add_sub_cancel_left : a + b - a = b :=
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lemma add_sub_cancel_left (a b : α) : a + b - a = b :=
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contravariant.add_le_cancellable.add_sub_cancel_left
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lemma le_sub_of_add_le_left' (h : a + b ≤ c) : b ≤ c - a :=
@@ -269,7 +269,7 @@ end contra
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section both
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variables [covariant_class α α (+) (≤)] [contravariant_class α α (+) (≤)]
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lemma add_sub_add_right_eq_sub' : (a + c) - (b + c) = a - b :=
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lemma add_sub_add_right_eq_sub' (a c b : α) : (a + c) - (b + c) = a - b :=
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begin
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apply le_antisymm,
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{ rw [sub_le_iff_left, add_right_comm], exact add_le_add_right le_add_sub c },
@@ -345,16 +345,16 @@ by { refine ((sub_le_sub_iff_right' h).mp h2.le).lt_of_ne _, rintro rfl, exact h
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lemma sub_eq_zero_iff_le : a - b = 0 ↔ a ≤ b :=
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by rw [← nonpos_iff_eq_zero, sub_le_iff_left, add_zero]
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@[simp] lemma sub_self' : a - a = 0 :=
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@[simp] lemma sub_self' (a : α) : a - a = 0 :=
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sub_eq_zero_iff_le.mpr le_rfl
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@[simp] lemma sub_le_self' : a - b ≤ a :=
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sub_le_iff_left.mpr $ le_add_left le_rfl
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@[simp] lemma sub_zero' : a - 0 = a :=
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@[simp] lemma sub_zero' (a : α) : a - 0 = a :=
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le_antisymm sub_le_self' $ le_add_sub.trans_eq $ zero_add _
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@[simp] lemma zero_sub' : 0 - a = 0 :=
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@[simp] lemma zero_sub' (a : α) : 0 - a = 0 :=
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sub_eq_zero_iff_le.mpr $ zero_le a
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lemma sub_self_add (a b : α) : a - (a + b) = 0 :=

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