27 lines
664 B
Text
27 lines
664 B
Text
import Std.Tactic.BVDecide
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open BitVec
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theorem arith_unit_1 (x y : BitVec 64) : x + y = y + x := by
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bv_decide
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theorem arith_unit_1' (x y : BitVec 64) : BitVec.add x y = y + x := by
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bv_decide
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theorem arith_unit_2 (x y : BitVec 64) : x - y = -y + x := by
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bv_decide
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theorem arith_unit_2' (x y : BitVec 64) : BitVec.sub x y = (BitVec.neg y) + x := by
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bv_decide
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theorem arith_unit_3 (x y : BitVec 16) : x - (x - y) = y := by
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bv_decide
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theorem arith_unit_4 (x y : BitVec 4) : x * y = y * x := by
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bv_decide
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theorem arith_unit_5 (x : BitVec 8) : x * 32 = 32 * x := by
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bv_decide
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theorem arith_unit_6 (x : BitVec 64) : x + x = 2 * x := by
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bv_decide
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