8c7f7484f9
Using the same strategy as #5852 this provides `bv_decide` support for `Bool` and `BitVec` ifs this in turn instantly enables support for: - `sdiv` - `smod` - `abs` and thus closes our last discrepancies to QF_BV!
41 lines
1.4 KiB
Text
41 lines
1.4 KiB
Text
import Std.Tactic.BVDecide
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open BitVec
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set_option bv.ac_nf false
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theorem substructure_unit_1 (x y z : BitVec 8) : ((x = y) ∧ (y = z)) ↔ ¬(¬(x =y) ∨ (¬(y = z))) := by
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bv_decide
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theorem substructure_unit_1' (x y z : BitVec 8) : ((x = y) && (y = z)) ↔ ¬(¬(x = y) || (!(y = z))) := by
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bv_decide
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theorem substructure_unit_1'' (x y z : BitVec 8) : (Bool.and (x = y) (y = z)) ↔ ¬(Bool.or (!(x = y)) (Bool.not (y = z))) := by
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bv_decide
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theorem substructure_unit_2 (x y : BitVec 8) : x = y → y = x := by
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bv_decide
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theorem substructure_unit_3 (x y : BitVec 8) : (x = y) ^^ (y ≠ x) := by
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bv_decide
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theorem substructure_unit_3' (x y : BitVec 8) : Bool.xor (x = y) (y ≠ x) := by
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bv_decide
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theorem substructure_unit_4 (a b : Bool) : (a && b) = (b && a) := by
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bv_decide
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theorem substructure_unit_5 (a : Bool) (b c : BitVec 32) (h1 : b < c ↔ a) (h2 : a = true) : b < c := by
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bv_decide
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theorem substructure_unit_6 (a b c: Bool) : (if a then b else c) = (if !a then c else b) := by
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bv_decide
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theorem substructure_unit_7 (a b c: Bool) : (bif a then b else c) = (bif !a then c else b) := by
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bv_decide
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theorem substructure_unit_8 (x : BitVec 32) : (if x.getLsbD 0 then !x.getLsbD 0 else x.getLsbD 0) = false := by
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bv_decide
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theorem substructure_unit_9 (x y : BitVec 32) (h : x.getLsbD 0 = false) : (if x.getLsbD 0 then x else y) = y := by
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bv_decide
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