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Proof step 8 from proof bor-2pot-plus-01 (previous step)

j < 2 ^ i, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i, j < 0 ⊦ bits2int(bitsinvert(bitsand(bitsinvert(sgn(bitsinvert(uint2bits(~(j * 2 ^ i))) +1)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
0 ≤ i, j < 0 ⊦ uint2bits(~(j * 2 ^ i)) = uint2bits(~ j) + mklist(false, i→n(i))
Proof step 10:
0 ≤ i ∧ j < 0, j < 2 ^ i, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i, j < 0 ⊦ bits2int(bitsinvert(bitsand(bitsinvert(sgn(bitsinvert(uint2bits(~ j) + mklist(false, i→n(i))) +1)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0

Rule argument

seq: 0 ≤ i, j < 0 ⊦ uint2bits(~(j * 2 ^ i)) = uint2bits(~ j) + mklist(false, i→n(i)) subst: [i, j] → [i, j] rotate: F spec: int2bits inst: name: uint2bits-2pot-06

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i, j