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Proof step 8 from proof band-011x-is-unsigned-fix (previous step)

# int2bits(j) < i→n(i), 0 < i ⊦ band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j))), i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ¬ false ∈ int2bits(i0).rest ∧ abs(j) ≤ 2 ^ n→i(# int2bits(i0) - 2) ∧ 0 < i0 → band(j, i0) = bits2uint(fillsgn(# int2bits(i0) - 1, int2bits(j)))
Proof step 10:
¬(¬ false ∈ int2bits(2 ^ i - 1).rest ∧ abs(j) ≤ 2 ^ n→i(# int2bits(2 ^ i - 1) - 2) ∧ 0 < 2 ^ i - 1), # int2bits(j) < i→n(i), 0 < i ⊦ band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j))), i = 0

Rule argument

name: band-011x-is-unsigned-01 rotate: F subst: [i0, j] → [2 ^ i - 1, j]

Additional information

Used simplifier rules: ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;%0 ≤ i ⊦ int2bits(2 ^ i - 1) = false ' + mklist(true, i→n(i));% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ 0 + m = m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: 2 ^ i - 1, j