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Proof step 14 from proof band-011x-is-unsigned (previous step)

0 ≤ 2 ^ i + j, 0 ≤ j + 2 ^ (i - 1), j < 0, 0 < i, 0 ≤ i ⊦ j + 2 ^ i = bits2int(fillsgn(i→n(i), int2bits(j))) + 2 ^ n→i(# fillsgn(i→n(i), int2bits(j))), fillsgn(i→n(i), int2bits(j)) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ # bits ≤ n → # fillsgn(n, bits) = n
Proof step 16:
¬ # int2bits(j) ≤ i→n(i), 0 ≤ 2 ^ i + j, 0 ≤ j + 2 ^ (i - 1), j < 0, 0 < i, 0 ≤ i ⊦ j + 2 ^ i = bits2int(fillsgn(i→n(i), int2bits(j))) + 2 ^ n→i(# fillsgn(i→n(i), int2bits(j))), fillsgn(i→n(i), int2bits(j)) = []
Proof step 22:
# int2bits(j) ≤ i→n(i), 0 ≤ 2 ^ i + j, 0 ≤ j + 2 ^ (i - 1), j < 0, 0 < i, 0 ≤ i ⊦ j + 2 ^ i = bits2int(fillsgn(i→n(i), int2bits(j))) + 2 ^ n→i(i→n(i)), fillsgn(i→n(i), int2bits(j)) = []

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [int2bits(j), i→n(i)] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used terms: int2bits(j), i→n(i)