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Proof step 67 from proof uint2bits-mod2pot (previous step)

false ' = sgn(false ' + lastn(i→n(i0), (uint2bits(i2) + mklist(false, i→n(i0))).rest)), 0 ≤ i2, 0 < i2, 0 ≤ 2 ^ i0, 1 < i2, 0 < 2 ^ i0, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n((i2 * 2 ^ i0 + 0) * 2 + 0) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ false ' = sgn(false ' + lastn(i→n(i0), (uint2bits(i2) + mklist(false, i→n(i0))).rest) + false '), ~1 = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ bits ≠ [] → (bits + bits0).rest = bits.rest + bits0

Rule argument

seq: ⊦ bits ≠ [] → (bits + bits0).rest = bits.rest + bits0 subst: [bits0, bits] → [mklist(false, i→n(i0)), uint2bits(i2)] rotate: F spec: list inst: bitlista name: rest-01

Additional information

Used simplifier rules: uint2bits-empty: 0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ lastn(n, bits + mklist(boolvar, n)) = mklist(boolvar, n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ sgn(false ' + mklist(false, n)) = false ';% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ sgn(boolvar ' + boolvar ' + bits) = sgn(boolvar ' + bits); Used terms: mklist(false, i→n(i0)), uint2bits(i2)