Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

[Merged by Bors] - feat(Data/Nat/Bitwise): add simp lemmas #17977

Closed
wants to merge 4 commits into from
Closed

[Merged by Bors] - feat(Data/Nat/Bitwise): add simp lemmas #17977

Changes from 2 commits
Commits
Show all changes
4 commits
Select commit Hold shift + click to select a range
ad80154
feat(Algebra/Group/Nat): add simp lemmas
pitmonticone Oct 20, 2024
94e9c33
move theorems to `Nat/Bitwise`
pitmonticone Oct 20, 2024
ba27a19
Update Mathlib/Data/Nat/Bitwise.lean
pitmonticone Oct 20, 2024
76e2b9e
Update Bitwise.lean
pitmonticone Oct 20, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
17 changes: 16 additions & 1 deletion Mathlib/Data/Nat/Bitwise.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -37,7 +37,6 @@ should be connected.
bitwise, and, or, xor
-/


open Function

namespace Nat
Expand Down Expand Up @@ -354,6 +353,22 @@ theorem lt_xor_cases {a b c : ℕ} (h : a < b ^^^ c) : a ^^^ c < b ∨ a ^^^ b <
obtain ha | hb | hc := xor_trichotomy <| Nat.xor_assoc _ _ _ ▸ xor_ne_zero.2 h.ne
exacts [(h.asymm ha).elim, Or.inl <| Nat.xor_comm _ _ ▸ hb, Or.inr hc]

@[simp]
theorem xor_mod_two_eq {m n : ℕ} : (m ^^^ n) % 2 = (m + n) % 2 := by
by_cases h : (m + n) % 2 = 0
· simp only [h, mod_two_eq_zero_iff_testBit_zero, testBit_zero, xor_mod_two_eq_one, decide_not,
Bool.decide_iff_dist, Bool.not_eq_false', beq_iff_eq, decide_eq_decide]
pitmonticone marked this conversation as resolved.
Show resolved Hide resolved
omega
· simp only [mod_two_ne_zero] at h
simp only [h, xor_mod_two_eq_one]
omega

@[simp]
theorem even_xor {m n : ℕ} : Even (m ^^^ n) ↔ (Even m ↔ Even n) := by
simp only [even_iff, xor_mod_two_eq]
simp only [← even_iff]
pitmonticone marked this conversation as resolved.
Show resolved Hide resolved
exact even_add

@[simp] theorem bit_lt_two_pow_succ_iff {b x n} : bit b x < 2 ^ (n + 1) ↔ x < 2 ^ n := by
cases b <;> simp <;> omega

Expand Down
Loading