refactor(library/data/nat,int): use nicer definitions of structure instances

library/data/int/basic.lean

@@ -27,7 +27,6 @@ following:
   padd_congr (p p' q q' : ℕ × ℕ) (H1 : p ≡ p') (H2 : q ≡ q') : padd p q ≡ p' q'
 
 -/
-
 import data.nat.basic data.nat.order data.nat.sub data.prod
 import algebra.relation algebra.binary algebra.ordered_ring
 import tools.fake_simplifier
@@ -612,9 +611,25 @@ section
   open [classes] algebra
 
   protected definition integral_domain [instance] [reducible] : algebra.integral_domain int :=
-  algebra.integral_domain.mk add add.assoc zero zero_add add_zero neg add.left_inv
+  ⦃algebra.integral_domain,
-  add.comm mul mul.assoc (of_num 1) one_mul mul_one mul.left_distrib mul.right_distrib
+    add            := add,
-  zero_ne_one mul.comm @eq_zero_or_eq_zero_of_mul_eq_zero
+    add_assoc      := add.assoc,
+    zero           := zero,
+    zero_add       := zero_add,
+    add_zero       := add_zero,
+    neg            := neg,
+    add_left_inv   := add.left_inv,
+    add_comm       := add.comm,
+    mul            := mul,
+    mul_assoc      := mul.assoc,
+    one            := (of_num 1),
+    one_mul        := one_mul,
+    mul_one        := mul_one,
+    left_distrib   := mul.left_distrib,
+    right_distrib  := mul.right_distrib,
+    zero_ne_one    := zero_ne_one,
+    mul_comm       := mul.comm,
+    eq_zero_or_eq_zero_of_mul_eq_zero := @eq_zero_or_eq_zero_of_mul_eq_zero⦄
 end
 
 /- instantiate ring theorems to int -/

library/data/int/order.lean

@@ -8,9 +8,7 @@ Authors: Floris van Doorn, Jeremy Avigad
 The order relation on the integers. We show that int is an instance of linear_comm_ordered_ring
 and transfer the results.
 -/
-
 import .basic algebra.ordered_ring
-
 open nat
 open decidable
 open fake_simplifier
@@ -216,11 +214,18 @@ section
 
   protected definition linear_ordered_comm_ring [instance] [reducible] :
     algebra.linear_ordered_comm_ring int :=
-  algebra.linear_ordered_comm_ring.mk add add.assoc zero zero_add add_zero neg add.left_inv
+  ⦃algebra.linear_ordered_comm_ring, int.integral_domain,
-    add.comm mul mul.assoc (of_num 1) one_mul mul_one mul.left_distrib mul.right_distrib
+    le               := le,
-    zero_ne_one le le.refl @le.trans @le.antisymm lt lt_iff_le_and_ne @add_le_add_left
+    le_refl          := le.refl,
-    @mul_nonneg @mul_pos le_iff_lt_or_eq le.total mul.comm
+    le_trans         := @le.trans,
-
+    le_antisymm      := @le.antisymm,
+    lt               := lt,
+    lt_iff_le_ne     := lt_iff_le_and_ne,
+    add_le_add_left  := @add_le_add_left,
+    mul_nonneg       := @mul_nonneg,
+    mul_pos          := @mul_pos,
+    le_iff_lt_or_eq  := le_iff_lt_or_eq,
+    le_total         := le.total⦄
 
   protected definition decidable_linear_ordered_comm_ring [instance] [reducible] :
     algebra.decidable_linear_ordered_comm_ring int :=

library/data/nat/basic.lean

@@ -291,9 +291,24 @@ section
   open [classes] algebra
 
   protected definition comm_semiring [instance] [reducible] : algebra.comm_semiring nat :=
-  algebra.comm_semiring.mk add add.assoc zero zero_add add_zero add.comm
+  ⦃algebra.comm_semiring,
-    mul mul.assoc (succ zero) one_mul mul_one mul.left_distrib mul.right_distrib
+    add            := add,
-    zero_mul mul_zero (ne.symm (succ_ne_zero zero)) mul.comm
+    add_assoc      := add.assoc,
+    zero           := zero,
+    zero_add       := zero_add,
+    add_zero       := add_zero,
+    add_comm       := add.comm,
+    mul            := mul,
+    mul_assoc      := mul.assoc,
+    one            := succ zero,
+    one_mul        := one_mul,
+    mul_one        := mul_one,
+    left_distrib   := mul.left_distrib,
+    right_distrib  := mul.right_distrib,
+    zero_mul       := zero_mul,
+    mul_zero       := mul_zero,
+    zero_ne_one    := ne.symm (succ_ne_zero zero),
+    mul_comm       := mul.comm⦄
 end
 
 section port_algebra