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Proof step 34 from proof bor-2pot-plus (previous step)

# int2bits(j0) = i→n(i) + 1, int2bits(j0) = boolvar ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, boolvar ∈ int2bits(j0), i→n(i) ≤ # bits ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bits) = j * 2 ^ i + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first → bits2int(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Proof step 36:
# bits ≠ 0 ∧ # uint2bits(j) ≠ 0 ∧ ¬ uint2bits(j).first, # int2bits(j0) = i→n(i) + 1, int2bits(j0) = boolvar ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, boolvar ∈ int2bits(j0), i→n(i) ≤ # bits ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2uint(uint2bits(j)) * 2 ^ n→i(# bits) + bits2uint(bits) = j * 2 ^ i + j0

Rule argument

seq: ⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first → bits2int(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0) subst: [bits0, bits] → [bits, uint2bits(j)] rotate: F spec: int2bits inst: name: bits2int-split

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ 0 ≤ j → ¬ uint2bits(j).first;% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ 0 ≤ j → bits2int(uint2bits(j)) = j;% ⊦ # [] = 0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);%0 ≤ i ⊦ i→n(i) ≤ (* m) ↔ i ≤ n→i(m);% ⊦ i < j → ¬ j < i; Used terms: bits, uint2bits(j)