c0617da18d
... while at it also call `trivial` to close goals that can be trivially closed. --------- Co-authored-by: Siddharth <siddu.druid@gmail.com> Co-authored-by: Henrik Böving <hargonix@gmail.com>
29 lines
919 B
Text
29 lines
919 B
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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