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chore: missing BitVec lemmas #5459

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Sep 25, 2024
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chore: missing BitVec lemmas #5459

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26 changes: 26 additions & 0 deletions src/Init/Data/BitVec/Lemmas.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -927,6 +927,10 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
ext
simp

@[simp] theorem not_allOnes : ~~~ allOnes w = 0#w := by
ext
simp

@[simp] theorem xor_allOnes {x : BitVec w} : x ^^^ allOnes w = ~~~ x := by
ext i
simp
Expand Down Expand Up @@ -1410,6 +1414,10 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
rw [getLsbD_append]
simpa using lt_of_getLsbD

@[simp] theorem zero_append_zero : 0#v ++ 0#w = 0#(v + w) := by
ext
simp only [getLsbD_append, getLsbD_zero, Bool.cond_self]

@[simp] theorem cast_append_right (h : w + v = w + v') (x : BitVec w) (y : BitVec v) :
cast h (x ++ y) = x ++ cast (by omega) y := by
ext
Expand Down Expand Up @@ -1655,6 +1663,10 @@ theorem getElem_concat (x : BitVec w) (b : Bool) (i : Nat) (h : i < w + 1) :
(concat x a) ^^^ (concat y b) = concat (x ^^^ y) (a ^^ b) := by
ext i; cases i using Fin.succRecOn <;> simp

@[simp] theorem zero_concat_false : concat 0#w false = 0#(w + 1) := by
ext
simp [getLsbD_concat]

/-! ### add -/

theorem add_def {n} (x y : BitVec n) : x + y = .ofNat n (x.toNat + y.toNat) := rfl
Expand Down Expand Up @@ -2166,6 +2178,20 @@ theorem twoPow_zero {w : Nat} : twoPow w 0 = 1#w := by
theorem getLsbD_one {w i : Nat} : (1#w).getLsbD i = (decide (0 < w) && decide (0 = i)) := by
rw [← twoPow_zero, getLsbD_twoPow]

@[simp] theorem true_cons_zero : cons true 0#w = twoPow (w + 1) w := by
ext
simp [getLsbD_cons]
omega

@[simp] theorem false_cons_zero : cons false 0#w = 0#(w + 1) := by
ext
simp [getLsbD_cons]

@[simp] theorem zero_concat_true : concat 0#w true = 1#(w + 1) := by
ext
simp [getLsbD_concat]
omega

/- ### setWidth, setWidth, and bitwise operations -/

/--
Expand Down
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