08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
169 lines
10 KiB
Text
169 lines
10 KiB
Text
theorem ex₁ : ∀ (x y z : Nat), max (0 + max x (max z (max (0 + 0) (max 1 0 + 0 + 0) * y))) y = max (max x y) z :=
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fun x y z =>
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Eq.mpr
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(id
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(congr
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(congrArg Eq
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(Eq.trans
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(congrFun'
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(congrArg max
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(Eq.trans
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(congrArg (HAdd.hAdd 0)
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(Eq.trans
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(congrArg (max x)
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(congrArg (max z)
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(Eq.trans
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(congrFun'
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(congrArg HMul.hMul
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(Eq.trans
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(congr
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(congrArg max
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((fun x inst =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := HAdd.hAdd, assoc := Nat.instAssociativeHAdd,
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comm := some { down := Nat.instCommutativeHAdd }, idem := none,
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vars := [{ value := x, neutral := some { down := inst } }],
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arbitrary := x }
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((Lean.Data.AC.Expr.var 0).op (Lean.Data.AC.Expr.var 0))
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(Lean.Data.AC.Expr.var 0) (Eq.refl true)))
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0 Nat.instLawfulIdentityHAddOfNat))
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(Eq.trans
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(congrFun'
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(congrArg HAdd.hAdd
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(congrFun'
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(congrArg HAdd.hAdd
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((fun x inst x_1 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := max, assoc := Nat.instAssociativeMax,
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comm := some { down := Nat.instCommutativeMax },
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idem := some { down := Nat.instIdempotentOpMax },
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vars :=
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[{ value := x, neutral := some { down := inst } },
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{ value := x_1, neutral := none }],
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arbitrary := x }
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((Lean.Data.AC.Expr.var 1).op (Lean.Data.AC.Expr.var 0))
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(Lean.Data.AC.Expr.var 1) (Eq.refl true)))
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0 Nat.instLawfulIdentityMaxOfNat 1))
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0))
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0)
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((fun x inst x_1 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := HAdd.hAdd, assoc := Nat.instAssociativeHAdd,
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comm := some { down := Nat.instCommutativeHAdd }, idem := none,
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vars :=
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[{ value := x, neutral := some { down := inst } },
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{ value := x_1, neutral := none }],
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arbitrary := x }
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(((Lean.Data.AC.Expr.var 1).op (Lean.Data.AC.Expr.var 0)).op
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(Lean.Data.AC.Expr.var 0))
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(Lean.Data.AC.Expr.var 1) (Eq.refl true)))
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0 Nat.instLawfulIdentityHAddOfNat 1)))
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((fun x inst x_1 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := max, assoc := Nat.instAssociativeMax,
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comm := some { down := Nat.instCommutativeMax },
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idem := some { down := Nat.instIdempotentOpMax },
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vars :=
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[{ value := x, neutral := some { down := inst } },
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{ value := x_1, neutral := none }],
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arbitrary := x }
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((Lean.Data.AC.Expr.var 0).op (Lean.Data.AC.Expr.var 1))
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(Lean.Data.AC.Expr.var 1) (Eq.refl true)))
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0 Nat.instLawfulIdentityMaxOfNat 1)))
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y)
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((fun x x_1 inst =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := HMul.hMul, assoc := Nat.instAssociativeHMul,
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comm := some { down := Nat.instCommutativeHMul }, idem := none,
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vars :=
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[{ value := x, neutral := none },
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{ value := x_1, neutral := some { down := inst } }],
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arbitrary := x }
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((Lean.Data.AC.Expr.var 1).op (Lean.Data.AC.Expr.var 0)) (Lean.Data.AC.Expr.var 0)
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(Eq.refl true)))
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y 1 Nat.instLawfulIdentityHMulOfNat))))
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((fun x x_1 x_2 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := max, assoc := Nat.instAssociativeMax,
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comm := some { down := Nat.instCommutativeMax },
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idem := some { down := Nat.instIdempotentOpMax },
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vars :=
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[{ value := x, neutral := none }, { value := x_1, neutral := none },
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{ value := x_2, neutral := none }],
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arbitrary := x }
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((Lean.Data.AC.Expr.var 0).op ((Lean.Data.AC.Expr.var 2).op (Lean.Data.AC.Expr.var 1)))
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((Lean.Data.AC.Expr.var 0).op ((Lean.Data.AC.Expr.var 1).op (Lean.Data.AC.Expr.var 2)))
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(Eq.refl true)))
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x y z)))
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((fun x inst x_1 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := HAdd.hAdd, assoc := Nat.instAssociativeHAdd,
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comm := some { down := Nat.instCommutativeHAdd }, idem := none,
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vars :=
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[{ value := x, neutral := some { down := inst } }, { value := x_1, neutral := none }],
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arbitrary := x }
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((Lean.Data.AC.Expr.var 0).op (Lean.Data.AC.Expr.var 1)) (Lean.Data.AC.Expr.var 1)
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(Eq.refl true)))
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0 Nat.instLawfulIdentityHAddOfNat (max x (max y z)))))
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y)
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((fun x x_1 x_2 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := max, assoc := Nat.instAssociativeMax, comm := some { down := Nat.instCommutativeMax },
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idem := some { down := Nat.instIdempotentOpMax },
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vars :=
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[{ value := x, neutral := none }, { value := x_1, neutral := none },
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{ value := x_2, neutral := none }],
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arbitrary := x }
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(((Lean.Data.AC.Expr.var 0).op ((Lean.Data.AC.Expr.var 1).op (Lean.Data.AC.Expr.var 2))).op
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(Lean.Data.AC.Expr.var 1))
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((Lean.Data.AC.Expr.var 0).op ((Lean.Data.AC.Expr.var 1).op (Lean.Data.AC.Expr.var 2)))
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(Eq.refl true)))
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x y z)))
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((fun x x_1 x_2 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := max, assoc := Nat.instAssociativeMax, comm := some { down := Nat.instCommutativeMax },
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idem := some { down := Nat.instIdempotentOpMax },
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vars :=
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[{ value := x, neutral := none }, { value := x_1, neutral := none },
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{ value := x_2, neutral := none }],
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arbitrary := x }
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(((Lean.Data.AC.Expr.var 0).op (Lean.Data.AC.Expr.var 1)).op (Lean.Data.AC.Expr.var 2))
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((Lean.Data.AC.Expr.var 0).op ((Lean.Data.AC.Expr.var 1).op (Lean.Data.AC.Expr.var 2))) (Eq.refl true)))
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x y z)))
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(Eq.refl (max x (max y z)))
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theorem ex₃ : ∀ (n : Nat), (fun x => n + x) = fun x => x + n :=
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fun n =>
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Eq.mpr
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(id
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(congr
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(congrArg Eq
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(funext fun x =>
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(fun x x_1 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := HAdd.hAdd, assoc := Nat.instAssociativeHAdd,
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comm := some { down := Nat.instCommutativeHAdd }, idem := none,
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vars := [{ value := x, neutral := none }, { value := x_1, neutral := none }], arbitrary := x }
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((Lean.Data.AC.Expr.var 0).op (Lean.Data.AC.Expr.var 1))
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((Lean.Data.AC.Expr.var 0).op (Lean.Data.AC.Expr.var 1)) (Eq.refl true)))
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n x))
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(funext fun x =>
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(fun x x_1 =>
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id
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(Lean.Data.AC.Context.eq_of_norm
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{ op := HAdd.hAdd, assoc := Nat.instAssociativeHAdd, comm := some { down := Nat.instCommutativeHAdd },
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idem := none, vars := [{ value := x, neutral := none }, { value := x_1, neutral := none }],
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arbitrary := x }
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((Lean.Data.AC.Expr.var 1).op (Lean.Data.AC.Expr.var 0))
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((Lean.Data.AC.Expr.var 0).op (Lean.Data.AC.Expr.var 1)) (Eq.refl true)))
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n x)))
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(Eq.refl fun x => n + x)
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