Operations for bit representation of Nat and BitVec.
#366
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Nat and BitVec.
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Nat and BitVec.Nat and BitVec.
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Co-authored-by: Scott Morrison <[email protected]>
Co-authored-by: Scott Morrison <[email protected]>
Co-authored-by: Scott Morrison <[email protected]>
Co-authored-by: Scott Morrison <[email protected]>
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@semorrison I think I've done all the changes you suggested. |
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| theorem testBit_bitwise | ||
| (false_false_axiom : f false false = false) (x y i : Nat) | ||
| : (bitwise f x y).testBit i = f (x.testBit i) (y.testBit i) := by | ||
| induction i using Nat.strongInductionOn generalizing x y with |
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This formatting looks pretty weird to me
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| theorem toNat_eq (x y : BitVec n) : x = y ↔ x.toNat = y.toNat := | ||
| Iff.intro (congrArg BitVec.toNat) eq_of_toNat_eq |
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Mathlib has this lemma, but calls it toNat_inj and states it in reverse.
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revert . fix a bit blech one more comment out broken and unused results chore: bump Std remove redundant simp lemmas cleanup fix: make `Nat.testBit_bitwise` a simp-lemma again. This fixes the Int.testbit_bitwise proofs fix `castNum_testBit` fix `testBit_eq_inth` fixes golf golf Apply suggestions from code review Co-authored-by: Eric Wieser <[email protected]> fix whitespace fix name conflict more efficient restore lemma feat: Mapping extreme points under continuous maps (#8574) Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme points of the image of that set. Also fix a few name and tweak the API a bit. Co-authored-by: Yury G. Kudryashov <[email protected]> chore(Profinite): allow more universe flexibility in Profinite/CofilteredLimit (#8613) We allow the indexing category for the cofiltered limit in the result `Profinite.exists_locallyConstant` to live in a smaller universe than our profinite sets. feat(CategoryTheory): `Preregular` and `FinitaryPreExtensive` implies `Precoherent` (#8643) We prove some results about effective epimorphisms which allow us to deduce that a category which is `FinitaryPreExtensive` and `Preregular` is also `Precoherent`. feat(Analysis/Seminorm): add more `*ball_smul_*ball` (#8724) We had `ball_smul_ball` and `closedBall_smul_closedBall`. Add versions with mixed `ball` and `closedBall`. Also move this lemmas below and golf the proofs. feat: the annihilator of the kernel of the trace form of a Lie module is contained in the span of its weights (#8739) fix breakage in BitVec lemmas
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revert . fix a bit blech one more comment out broken and unused results chore: bump Std remove redundant simp lemmas cleanup fix: make `Nat.testBit_bitwise` a simp-lemma again. This fixes the Int.testbit_bitwise proofs fix `castNum_testBit` fix `testBit_eq_inth` fixes golf golf Apply suggestions from code review Co-authored-by: Eric Wieser <[email protected]> fix whitespace fix name conflict more efficient restore lemma feat: Mapping extreme points under continuous maps (#8574) Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme points of the image of that set. Also fix a few name and tweak the API a bit. Co-authored-by: Yury G. Kudryashov <[email protected]> chore(Profinite): allow more universe flexibility in Profinite/CofilteredLimit (#8613) We allow the indexing category for the cofiltered limit in the result `Profinite.exists_locallyConstant` to live in a smaller universe than our profinite sets. feat(CategoryTheory): `Preregular` and `FinitaryPreExtensive` implies `Precoherent` (#8643) We prove some results about effective epimorphisms which allow us to deduce that a category which is `FinitaryPreExtensive` and `Preregular` is also `Precoherent`. feat(Analysis/Seminorm): add more `*ball_smul_*ball` (#8724) We had `ball_smul_ball` and `closedBall_smul_closedBall`. Add versions with mixed `ball` and `closedBall`. Also move this lemmas below and golf the proofs. feat: the annihilator of the kernel of the trace form of a Lie module is contained in the span of its weights (#8739) fix breakage in BitVec lemmas
eric-wieser
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| else | ||
| simp [h] | ||
|
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| theorem toNat_append (x : BitVec m) (y : BitVec n) : (x ++ y).toNat = x.toNat <<< n ||| y.toNat := |
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In mathlib this had arguments msbs and lsbs for clarity; it feels like a regression to rename them back to x and y.
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Notably leanprover-community/batteries#366 changed the definition of `testBit` (to something equivalent) when upstreaming it, which broke a handful of proofs. Other conflicting changes in Std, resolved for now by priming the mathlib name: * `Std.BitVec.adc`: the type was changed from `BitVec (n + 1)` to `Bool × BitVec w` * `Nat.mul_add_mod`: the type was changed from `(a * b + c) % b = c % b` to `(b * a + c) % b = c % b` [Zulip thread](https://leanprover.zulipchat.com/#narrow/stream/348111-std4/topic/Mathlib.20bump.20for.20.22Operations.20for.20bit.20representation.20of.20.2E.2E.2E.22/near/404801443) Co-authored-by: Scott Morrison <[email protected]> Co-authored-by: Alex Keizer <[email protected]> Co-authored-by: Eric Wieser <[email protected]>
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Notably leanprover-community/batteries#366 changed the definition of `testBit` (to something equivalent) when upstreaming it, which broke a handful of proofs. Other conflicting changes in Std, resolved for now by priming the mathlib name: * `Std.BitVec.adc`: the type was changed from `BitVec (n + 1)` to `Bool × BitVec w` * `Nat.mul_add_mod`: the type was changed from `(a * b + c) % b = c % b` to `(b * a + c) % b = c % b` [Zulip thread](https://leanprover.zulipchat.com/#narrow/stream/348111-std4/topic/Mathlib.20bump.20for.20.22Operations.20for.20bit.20representation.20of.20.2E.2E.2E.22/near/404801443) Co-authored-by: Scott Morrison <[email protected]> Co-authored-by: Alex Keizer <[email protected]> Co-authored-by: Eric Wieser <[email protected]>
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This is a large PR that has operations for working with Nat and BitVec as functions from indices to Bool. In particular it builds upon work in #314 and #358