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Proof step 14 from proof bor-2pot-plus (previous step)

0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j ⊦ bits2int(bitsinvert(bitsand(bitsinvert(uint2bits(j)) + mklist(true, i→n(i)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 16:
bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) ≠ [] ∧ bitsinvert(int2bits(j0)) ≠ [], 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j ⊦ bits2int(bitsinvert(bitsand(bitsinvert(int2bits(j0)), bitsinvert(uint2bits(j)) + mklist(true, i→n(i))))) = j * 2 ^ i + j0

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [bitsinvert(int2bits(j0)), bitsinvert(uint2bits(j)) + mklist(true, i→n(i))]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ int2bits(j) ≠ []; Used terms: bitsinvert(int2bits(j0)), bitsinvert(uint2bits(j)) + mklist(true, i→n(i))