@@ -434,96 +434,104 @@ noncomputable def foo : ℝ := 1
434434example : foo = 1 := by norm_num [foo]
435435
436436section
437- variable [AddMonoidWithOne α]
438- example : (1 + 0 : α) = (0 + 1 : α) := by norm_num1
439- example : (0 + (2 + 3 ) + 1 : α) = 6 := by norm_num1
437+
438+ variable [AddMonoidWithOne α]
439+ example : (1 + 0 : α) = (0 + 1 : α) := by norm_num1
440+ example : (0 + (2 + 3 ) + 1 : α) = 6 := by norm_num1
441+
440442end
441443
442444section
443- variable [Semiring α]
444- example : (70 * (33 + 2 ) : α) = 2450 := by norm_num1
445- example : (8 + 2 ^ 2 * 3 : α) = 20 := by norm_num1
446- example : ((2 * 1 + 1 ) ^ 2 : α) = (3 * 3 : α) := by norm_num1
445+
446+ variable [Semiring α]
447+ example : (70 * (33 + 2 ) : α) = 2450 := by norm_num1
448+ example : (8 + 2 ^ 2 * 3 : α) = 20 := by norm_num1
449+ example : ((2 * 1 + 1 ) ^ 2 : α) = (3 * 3 : α) := by norm_num1
447450end
451+
448452section
449- variable [Ring α]
450-
451- example : (-1 : α) * 1 = -1 := by norm_num1
452- example : (-2 : α) * 1 = -2 := by norm_num1
453- example : (-2 : α) * -1 = 2 := by norm_num1
454- example : (-2 : α) * -2 = 4 := by norm_num1
455- example : (1 : α) * 0 = 0 := by norm_num1
456-
457- example : ((1 : α) + 1 ) * 5 = 6 + 4 := by norm_num1
458-
459- example : (1 : α) = 0 + 1 := by norm_num1
460- example : (1 : α) = 1 + 0 := by norm_num1
461- example : (2 : α) = 1 + 1 := by norm_num1
462- example : (2 : α) = 0 + 2 := by norm_num1
463- example : (3 : α) = 1 + 2 := by norm_num1
464- example : (3 : α) = 2 + 1 := by norm_num1
465- example : (4 : α) = 3 + 1 := by norm_num1
466- example : (4 : α) = 2 + 2 := by norm_num1
467- example : (5 : α) = 4 + 1 := by norm_num1
468- example : (5 : α) = 3 + 2 := by norm_num1
469- example : (5 : α) = 2 + 3 := by norm_num1
470- example : (6 : α) = 0 + 6 := by norm_num1
471- example : (6 : α) = 3 + 3 := by norm_num1
472- example : (6 : α) = 4 + 2 := by norm_num1
473- example : (6 : α) = 5 + 1 := by norm_num1
474- example : (7 : α) = 4 + 3 := by norm_num1
475- example : (7 : α) = 1 + 6 := by norm_num1
476- example : (7 : α) = 6 + 1 := by norm_num1
477- example : 33 = 5 + (28 : α) := by norm_num1
478-
479- example : (12 : α) = 0 + (2 + 3 ) + 7 := by norm_num1
480- example : (105 : α) = 70 + (33 + 2 ) := by norm_num1
481-
482- example : (45000000000 : α) = 23000000000 + 22000000000 := by norm_num1
483-
484- example : (0 : α) - 3 = -3 := by norm_num1
485- example : (0 : α) - 2 = -2 := by norm_num1
486- example : (1 : α) - 3 = -2 := by norm_num1
487- example : (1 : α) - 1 = 0 := by norm_num1
488- example : (0 : α) - 3 = -3 := by norm_num1
489- example : (0 : α) - 3 = -3 := by norm_num1
490- example : (12 : α) - 4 - (5 + -2 ) = 5 := by norm_num1
491- example : (12 : α) - 4 - (5 + -2 ) - 20 = -15 := by norm_num1
492-
493- example : (0 : α) * 0 = 0 := by norm_num1
494- example : (0 : α) * 1 = 0 := by norm_num1
495- example : (0 : α) * 2 = 0 := by norm_num1
496- example : (2 : α) * 0 = 0 := by norm_num1
497- example : (1 : α) * 0 = 0 := by norm_num1
498- example : (1 : α) * 1 = 1 := by norm_num1
499- example : (2 : α) * 1 = 2 := by norm_num1
500- example : (1 : α) * 2 = 2 := by norm_num1
501- example : (2 : α) * 2 = 4 := by norm_num1
502- example : (3 : α) * 2 = 6 := by norm_num1
503- example : (2 : α) * 3 = 6 := by norm_num1
504- example : (4 : α) * 1 = 4 := by norm_num1
505- example : (1 : α) * 4 = 4 := by norm_num1
506- example : (3 : α) * 3 = 9 := by norm_num1
507- example : (3 : α) * 4 = 12 := by norm_num1
508- example : (4 : α) * 4 = 16 := by norm_num1
509- example : (11 : α) * 2 = 22 := by norm_num1
510- example : (15 : α) * 6 = 90 := by norm_num1
511- example : (123456 : α) * 123456 = 15241383936 := by norm_num1
453+
454+ variable [Ring α]
455+
456+ example : (-1 : α) * 1 = -1 := by norm_num1
457+ example : (-2 : α) * 1 = -2 := by norm_num1
458+ example : (-2 : α) * -1 = 2 := by norm_num1
459+ example : (-2 : α) * -2 = 4 := by norm_num1
460+ example : (1 : α) * 0 = 0 := by norm_num1
461+
462+ example : ((1 : α) + 1 ) * 5 = 6 + 4 := by norm_num1
463+
464+ example : (1 : α) = 0 + 1 := by norm_num1
465+ example : (1 : α) = 1 + 0 := by norm_num1
466+ example : (2 : α) = 1 + 1 := by norm_num1
467+ example : (2 : α) = 0 + 2 := by norm_num1
468+ example : (3 : α) = 1 + 2 := by norm_num1
469+ example : (3 : α) = 2 + 1 := by norm_num1
470+ example : (4 : α) = 3 + 1 := by norm_num1
471+ example : (4 : α) = 2 + 2 := by norm_num1
472+ example : (5 : α) = 4 + 1 := by norm_num1
473+ example : (5 : α) = 3 + 2 := by norm_num1
474+ example : (5 : α) = 2 + 3 := by norm_num1
475+ example : (6 : α) = 0 + 6 := by norm_num1
476+ example : (6 : α) = 3 + 3 := by norm_num1
477+ example : (6 : α) = 4 + 2 := by norm_num1
478+ example : (6 : α) = 5 + 1 := by norm_num1
479+ example : (7 : α) = 4 + 3 := by norm_num1
480+ example : (7 : α) = 1 + 6 := by norm_num1
481+ example : (7 : α) = 6 + 1 := by norm_num1
482+ example : 33 = 5 + (28 : α) := by norm_num1
483+
484+ example : (12 : α) = 0 + (2 + 3 ) + 7 := by norm_num1
485+ example : (105 : α) = 70 + (33 + 2 ) := by norm_num1
486+
487+ example : (45000000000 : α) = 23000000000 + 22000000000 := by norm_num1
488+
489+ example : (0 : α) - 3 = -3 := by norm_num1
490+ example : (0 : α) - 2 = -2 := by norm_num1
491+ example : (1 : α) - 3 = -2 := by norm_num1
492+ example : (1 : α) - 1 = 0 := by norm_num1
493+ example : (0 : α) - 3 = -3 := by norm_num1
494+ example : (0 : α) - 3 = -3 := by norm_num1
495+ example : (12 : α) - 4 - (5 + -2 ) = 5 := by norm_num1
496+ example : (12 : α) - 4 - (5 + -2 ) - 20 = -15 := by norm_num1
497+
498+ example : (0 : α) * 0 = 0 := by norm_num1
499+ example : (0 : α) * 1 = 0 := by norm_num1
500+ example : (0 : α) * 2 = 0 := by norm_num1
501+ example : (2 : α) * 0 = 0 := by norm_num1
502+ example : (1 : α) * 0 = 0 := by norm_num1
503+ example : (1 : α) * 1 = 1 := by norm_num1
504+ example : (2 : α) * 1 = 2 := by norm_num1
505+ example : (1 : α) * 2 = 2 := by norm_num1
506+ example : (2 : α) * 2 = 4 := by norm_num1
507+ example : (3 : α) * 2 = 6 := by norm_num1
508+ example : (2 : α) * 3 = 6 := by norm_num1
509+ example : (4 : α) * 1 = 4 := by norm_num1
510+ example : (1 : α) * 4 = 4 := by norm_num1
511+ example : (3 : α) * 3 = 9 := by norm_num1
512+ example : (3 : α) * 4 = 12 := by norm_num1
513+ example : (4 : α) * 4 = 16 := by norm_num1
514+ example : (11 : α) * 2 = 22 := by norm_num1
515+ example : (15 : α) * 6 = 90 := by norm_num1
516+ example : (123456 : α) * 123456 = 15241383936 := by norm_num1
517+
512518end
513519
514520section
515- variable [Field α] [LinearOrder α] [IsStrictOrderedRing α]
516- example : (4 : α) / 2 = 2 := by norm_num1
517- example : (4 : α) / 1 = 4 := by norm_num1
518- example : (4 : α) / 3 = 4 / 3 := by norm_num1
519- example : (50 : α) / 5 = 10 := by norm_num1
520- example : (1056 : α) / 1 = 1056 := by norm_num1
521- example : (6 : α) / 4 = 3 /2 := by norm_num1
522- example : (0 : α) / 3 = 0 := by norm_num1
523- example : (3 : α) / 0 = 0 := by norm_num1
524- example : (9 * 9 * 9 ) * (12 : α) / 27 = 81 * (2 + 2 ) := by norm_num1
525- example : (-2 : α) * 4 / 3 = -8 / 3 := by norm_num1
526- example : - (-4 / 3 ) = 1 / (3 / (4 : α)) := by norm_num1
521+
522+ variable [Field α] [LinearOrder α] [IsStrictOrderedRing α]
523+ example : (4 : α) / 2 = 2 := by norm_num1
524+ example : (4 : α) / 1 = 4 := by norm_num1
525+ example : (4 : α) / 3 = 4 / 3 := by norm_num1
526+ example : (50 : α) / 5 = 10 := by norm_num1
527+ example : (1056 : α) / 1 = 1056 := by norm_num1
528+ example : (6 : α) / 4 = 3 /2 := by norm_num1
529+ example : (0 : α) / 3 = 0 := by norm_num1
530+ example : (3 : α) / 0 = 0 := by norm_num1
531+ example : (9 * 9 * 9 ) * (12 : α) / 27 = 81 * (2 + 2 ) := by norm_num1
532+ example : (-2 : α) * 4 / 3 = -8 / 3 := by norm_num1
533+ example : - (-4 / 3 ) = 1 / (3 / (4 : α)) := by norm_num1
534+
527535end
528536
529537-- user command
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