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Proof step 101 from proof cast-mod-neg-high (previous step)

~1 = j % 2 ^ i, i→n(i) = # int2bits(~1).rest, 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), j < 0, j + 2 ^ i ≤ 0, j + 2 ^ i < i, i→n(i) < # int2bits(~1), j + 1 < 2 ^ (i - 1), 0 < i, j < ~1, j + 2 ^ i < 2 ^ (i - 1) ⊦ i = 1, j = ~1, bits2int(int2bits(~1).rest) = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 102:
⊦ i + 1 = 0 → int2bits(i) = true '

Rule argument

seq: ⊦ i + 1 = 0 → int2bits(i) = true ' subst: [i] → [~1] rotate: F spec: int2bits inst: name: int2bits-mone

Additional information

Used simplifier rules: ⊦ boolvar '.rest = [];% ⊦ # [] = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ # boolvar ' = 0 +1;%0 ≤ i ⊦ i→n(i) < (* m) ↔ i < n→i(m);% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: ~1