30 lines
868 B
Text
30 lines
868 B
Text
import Std.Tactic.BVDecide
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open BitVec
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theorem bitwise_unit_1 {x y : BitVec 64} : ~~~(x &&& y) = (~~~x ||| ~~~y) := by
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bv_decide
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theorem bitwise_unit_1' {x y : BitVec 64} : ~~~(BitVec.and x y) = ((BitVec.not x) ||| ~~~y) := by
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bv_decide
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theorem bitwise_unit_2 {x : BitVec 64} : x ^^^ x = 0 := by
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bv_decide
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theorem bitwise_unit_2' {x : BitVec 64} : (BitVec.xor x x) = 0 := by
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bv_decide
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theorem bitwise_unit_3 {x : BitVec 64} : (x ^^^ x).getLsb 32 = false := by
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bv_decide
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theorem bitwise_unit_4 {x : BitVec 64} : (x ^^^ ~~~x).getLsb 32 = true := by
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bv_decide
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theorem bitwise_unit_5 {x : BitVec 64} : (x ^^^ ~~~x).getLsb 128 = false := by
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bv_decide
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theorem bitwise_unit_6 {x : BitVec 64} : (x ^^^ ~~~x).getLsb 63 = (x ^^^ ~~~x).msb := by
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bv_decide
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theorem bitwise_unit_7 (x : BitVec 32) : x ^^^ 123#32 = 123#'(by decide) ^^^ x := by
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bv_decide
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