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Proof step 20 from proof bib-neg-low (previous step)

j < ~1, # int2bits(j) = 9, j < 0, ~256 < j, j < ~128 ⊦ b2i(i2b(j + 2 ^ (n→i(# int2bits(j)) - 1))) = 256 + j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
0 ≤ i, ~(2 ^ (i + 1)) ≤ j, j < ~(2 ^ i) ⊦ # int2bits(j) = i→n(i + 2)
Proof step 22:
0 ≤ 7 ∧ ~(2 ^ (7 + 1)) ≤ j ∧ j < ~(2 ^ 7), j < ~1, i→n(7 + 2) = 9, j < 0, ~256 < j, j < ~128 ⊦ b2i(i2b(j + 2 ^ (n→i(i→n(7 + 2)) - 1))) = 256 + j

Rule argument

seq: 0 ≤ i, ~(2 ^ (i + 1)) ≤ j, j < ~(2 ^ i) ⊦ # int2bits(j) = i→n(i + 2) subst: [i, j] → [7, j] rotate: F spec: int2bits inst: name: int2bits-len-neg

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); Used terms: 7, j