This PR also pulls in some mathlib theorems on testBit and Nat and establishes facts about 2^w that are needed here and which are generally useful for bitvector reasoning.
The following theorem is not generalized to arbitrary x instead of 2, as this would require a condition to be added for x > 1 which would have to be passed to simp each time this theorem should fire.
chore: derive from testBit_two_pow
chore: convert first to prop and then decide
chore: move intMax down as well
chore: add simp set
Add simp-set into this PR
chore: fix simp extension
Move file to src/Lean to fix build
Add prelude
update date
Add university of cambridge as copyright holder
improve naming
use whitespace uniformly
use decide (n = m)
Drop the 'Nat.' namespace
Update src/Init/Data/BitVec/Lemmas.lean
Co-authored-by: Siddharth <siddu.druid@gmail.com>
Update src/Init/Data/BitVec/Lemmas.lean
Co-authored-by: Siddharth <siddu.druid@gmail.com>
Fix build
add some theorems
Revert "add some theorems"
This reverts commit fb97bc2007e371854b40badb3d6014da034c1f5e.
WIP
Shorten proof
Update src/Init/Data/Nat/Lemmas.lean
finish proofs
Update src/Init/Data/BitVec/Lemmas.lean
Co-authored-by: Kim Morrison <scott@tqft.net>
Update src/Init/Data/Nat/Lemmas.lean
Co-authored-by: Kim Morrison <scott@tqft.net>
chore: move BoolToPropSimps
`simp only` will not apply this simproc anymore. Users must now write
`simp only [reduceCtorEq]`. See RFC #5046 for motivation.
This PR also renames simproc to `reduceCtorEq`.
close#5046
@semorrison A few `simp only ...` tactics will probably break in
Mathlib. Fix: include `reduceCtorEq`.
This allows bitblasting `BitVec.replicate`.
I changed the definition of `BitVec.replicate` to use `BitVec.cast` in
order to make the proof smoother, since it's an easier time simplifying
away terms with `BitVec.cast`.
---------
Co-authored-by: Tobias Grosser <tobias@grosser.es>
We add a new definition `BitVec.twoPow w i` to represent `(1#w <<< i)`.
This expression is used to test bits when building the multiplication
bitblaster.
Patch 1/?, being peeled from https://github.com/opencompl/lean4/pull/6.
---------
Co-authored-by: Tobias Grosser <github@grosser.es>
This PR introduces complete simprocs for all the Int versions of
div/mod, and makes some small refactoring of Int lemmas and
library_search.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
The linters in Batteries can be used to spot mistakes in Lean. See the
message on
[Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Go-to-def.20on.20typeclass.20fields.20and.20type-dependent.20notation/near/442613564).
These are the different linters with errors:
- unusedArguments:
There are many unused instance arguments, especially a redundant `[Monad
m]` is very common
- checkUnivs:
There was a problem with universes in a definition in
`Init.Control.StateCps`. I fixed it by adding a `variable` statement for
the implicit arguments in the file.
- defLemma:
many proofs are written as `def` instead of `theorem`, most notably
`rfl`. Because `rfl` is used as a match pattern, it must be a def. Is
this desirable?
The keyword `abbrev` is sometimes used for an alias of a theorem, which
also results in a def. I would want to replace it with the `alias`
keyword to fix this, but it isn't available.
- dupNamespace:
I fixed some of these, but left `Tactic.Tactic` and `Parser.Parser` as
they are as these seem intended.
- unusedHaveSuffices:
I cleaned up a few proofs with unused `have` or `suffices`
- explicitVarsOfIff:
I didn't fix any of these, because that would be a breaking change.
- simpNF:
I didn't fix any of these, because I think that requires knowing the
intended simplification order.
`Nat.succ_eq_add_one` and `Nat.pred_eq_sub_one` are now simp lemmas. For
theorems about `Nat.succ` or `Nat.pred` without corresponding theorem
for `+ 1` or `- 1`, this adds the corresponding theorem.
Given `h` with type `x + k = y + k'` (or `h : k = k')`, `cases h`
produced a proof of size linear in `min k k'`. `isDefEq` has support for
offset, but `unifyEq?` did not have it, and a stack overflow occurred
while processing the resulting proof. This PR fixes this issue.
closes#4219
Show that shifting a natural number left and then shifting right by the
same amount is a no-op.
I originally proved this in a different PR, ended up not needing the
fact after all, but it still seemed like a generally useful simp lemma
to have.
