2015-11-29 05:33:09 +00:00
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-- Test [light] annotation
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-- Remark: it will take some additional work to get ⁻¹ to rewrite well
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-- when there is a proof obligation.
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2015-12-05 01:57:03 +00:00
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import algebra.ring algebra.field data.set data.finset
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open algebra
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2015-11-29 05:33:09 +00:00
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attribute neg [light 2]
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attribute inv [light 2]
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attribute add.right_inv [simp]
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attribute add_neg_cancel_left [simp]
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attribute mul.right_inv [simp]
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attribute mul_inv_cancel_left [simp]
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2015-12-05 01:57:03 +00:00
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open simplifier.unit simplifier.ac
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2015-11-29 05:33:09 +00:00
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namespace ag
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universe l
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constants (A : Type.{l}) (s1 : add_comm_group A) (s2 : has_one A)
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attribute s1 [instance]
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attribute s2 [instance]
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constants (x y z w v : A)
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#simplify eq env 0 x + y + - x + -y + z + -z
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#simplify eq env 0 -100 + -v + -v + x + -v + y + - x + -y + z + -z + v + v + v + 100
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end ag
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namespace mg
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universe l
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constants (A : Type.{l}) (s1 : comm_group A) (s2 : has_add A)
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attribute s1 [instance]
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attribute s2 [instance]
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constants (x y z w v : A)
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#simplify eq env 0 x⁻¹ * y⁻¹ * z⁻¹ * 100⁻¹ * x * y * z * 100
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end mg
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namespace s
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open set
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universe l
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constants (A : Type.{l}) (x y z v w : set A)
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attribute complement [light 1]
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-- TODO(dhs, leo): Where do we put this group of simp rules?
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attribute union_comp_self [simp]
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lemma union_comp_self_left [simp] {X : Type} (s t : set X) : s ∪ (-s ∪ t)= univ := sorry
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attribute union.comm [simp]
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attribute union.assoc [simp]
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attribute union.left_comm [simp]
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#simplify eq env 0 x ∪ y ∪ z ∪ -x
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attribute inter_comp_self [simp]
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lemma inter_comp_self_left [simp] {X : Type} (s t : set X) : s ∩ (-s ∩ t)= empty := sorry
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attribute inter.comm [simp]
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attribute inter.assoc [simp]
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attribute inter.left_comm [simp]
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#simplify eq env 0 x ∩ y ∩ z ∩ -x
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end s
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