lemma
proved
tactic proof
allOnes_testBit_eq_false_at
show as:
view Lean formalization →
formal statement (Lean)
103private lemma allOnes_testBit_eq_false_at (t : Nat) : (allOnes t).testBit t = false := by
proof body
Tactic-mode proof.
104 -- `allOnes t < 2^t`
105 have hlt : allOnes t < 2 ^ t := by
106 -- `2^t - 1 < 2^t` since `2^t > 0`
107 simpa [allOnes] using Nat.sub_lt (pow_pos (by decide : 0 < (2 : Nat)) t) (by decide : 0 < 1)
108 exact Nat.testBit_eq_false_of_lt hlt
109