6080e3dd5c
Closes #2736 See comment at `ExprDefEq.lean` for explanation. Side effects: - Improved error messages in two tests. - Had to improve `getSuccesses` procedure at `App.lean`. It now discards candidates that contain postponed elaboration problems. If it is too disruptive for Mathlib, we should try to discard the ones that have postponed metavariables.
72 lines
1.8 KiB
Text
72 lines
1.8 KiB
Text
set_option autoImplicit true
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section Mathlib.Init.ZeroOne
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class One (α : Type) where
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one : α
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instance One.toOfNat1 {α} [One α] : OfNat α (nat_lit 1) where
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ofNat := ‹One α›.1
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end Mathlib.Init.ZeroOne
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section Mathlib.Algebra.Group.Defs
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class MulOneClass (M : Type) extends One M, Mul M where
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one_mul : ∀ a : M, 1 * a = a
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export MulOneClass (one_mul)
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end Mathlib.Algebra.Group.Defs
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section Mathlib.Algebra.Ring.Defs
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class Distrib (R : Type) extends Mul R, Add R where
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right_distrib : ∀ a b c : R, (a + b) * c = a * c + b * c
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class RightDistribClass (R : Type) [Mul R] [Add R] : Prop where
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right_distrib : ∀ a b c : R, (a + b) * c = a * c + b * c
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instance Distrib.rightDistribClass (R : Type) [Distrib R] : RightDistribClass R :=
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⟨Distrib.right_distrib⟩
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theorem add_mul [Mul R] [Add R] [RightDistribClass R] (a b c : R) :
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(a + b) * c = a * c + b * c :=
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RightDistribClass.right_distrib a b c
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theorem add_one_mul [Add α] [MulOneClass α] [RightDistribClass α] (a b : α) :
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(a + 1) * b = a * b + b := by
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rw [add_mul, one_mul]
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class Semiring (R : Type) extends Distrib R, MulOneClass R
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end Mathlib.Algebra.Ring.Defs
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section Mathlib.Data.Nat.Basic
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instance : Semiring Nat where
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add := Nat.add
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mul := Nat.mul
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one := Nat.succ Nat.zero
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one_mul := sorry
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right_distrib := sorry
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end Mathlib.Data.Nat.Basic
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#synth MulOneClass Nat -- works
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#synth RightDistribClass Nat -- works
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theorem ex1 [Add α] [MulOneClass α] [RightDistribClass α] (a b : α) :
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(a + 1) * b = a * b + b := by
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sorry
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#check (ex1) -- should work
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#check (add_one_mul) -- should work
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#check @add_one_mul
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example {a b : Nat} : (a + 1) * b = a * b + b := by
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have := add_one_mul a b -- works
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rw [add_one_mul] -- should work
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example {a b : Nat} : (a + 1) * b = a * b + b := by
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rw [add_one_mul] -- should work
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