feat: BitVec.shiftLeft_shiftLeft, BitVec.shiftRight_shiftRight #4148
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As requested by @hargoniX, closes two `sorry`s at https://github.com/leanprover/leansat/pull/64/files.
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semorrison
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May 13, 2024
semorrison
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May 13, 2024
src/Init/Data/BitVec/Lemmas.lean
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| -- omega claims that the system cannot be proven, so we case bash. | ||
| -- The entire proof below should be redundant once omega is complete. |
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decide statements are out of scope for omega!
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If you want to case bash and then hand off to omega, use:
theorem BitVec.shiftLeft_shiftLeft (w : Nat) (x : BitVec w) (n m : Nat) :
(x <<< n) <<< m = x <<< (n + m) := by
ext i
simp only [getLsb_shiftLeft, Fin.is_lt, decide_True, Bool.true_and]
rw [show i - (n + m) = (i - m - n) by omega]
cases h₂ : decide (i < m) <;> cases h₃ : decide (i - m < w) <;> cases h₄ : decide (i - m < n) <;> cases h₅ : decide (i < n + m) <;>
simp at * <;> omega
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Sweet, thanks for the tutorial! rw [show _ by omega] is a neat one, I'm going to remember this golf trick :)
Co-authored-by: Kim Morrison <[email protected]>
As taught by Kim Morrison.
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Fixes double namespace introduced in #4148
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Closes two
sorrys at https://github.com/leanprover/leansat/pull/64/files.