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Proof step 53 from proof bor-2pot-plus (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ mklist(boolvar, 0) = [];% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i = i + j ↔ j = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ 0 ≤ i → (i < 1 ↔ i = 0); Used terms: mklist(true, i→n(i)), bitsinvert(int2bits(j0))