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Proof step 68 from proof shiftright-rec-neg (previous step)

int2bits(i % 2).butlast = [], abs(j) = 1, i < ~1, i < 0 ⊦ int2bits((i - 1) / 2) + int2bits(i % 2) = [], j = 0, bits2int(true ' + int2bits((i - 1) / 2)) = (i - 1) / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 69:
⊦ i < 0 → bits2int(true ' + int2bits(i)) = i

Rule argument

seq: ⊦ i < 0 → bits2int(true ' + int2bits(i)) = i subst: [i] → [(i - 1) / 2] rotate: F spec: int2bits inst: name: bits2int-neg-1bit

Additional information

Used simplifier rules: 0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0;% ⊦ i + (j - i0) = i + j - i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ i ≤ ~1 ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: (i - 1) / 2