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Proof step 47 from proof cast-mod-neg-high (previous step)

j % 2 ^ i = 0, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 0 ≤ 2 ^ (i - 1), j < 0, 0 < i, 2 ^ (i - 1) + j < 0 ⊦ j = ~1, i = 1, bits2int(mklist(false, i→n(i))) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ ¬ true ∈ bits ∧ bits ≠ [] → bits2int(bits) = 0

Rule argument

seq: ⊦ ¬ true ∈ bits ∧ bits ≠ [] → bits2int(bits) = 0 subst: [bits] → [mklist(false, i→n(i))] rotate: F spec: int2bits inst: name: bits2int-zero-01

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ true ∈ mklist(false, n);% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ i % 1 = 0;% ⊦ mklist(boolvar, 0) = [];% ⊦ i + 0 = i;% ⊦ i < 0 ∧ 0 ≤ j → i < j; Used terms: mklist(false, i→n(i))