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Proof step 24 from proof int2bits-rest (previous step)

(sgn(bitsinvert(uint2bits(~(j / 2)))) + true ').rest = [], j < 0, j < ~1, true ∈ uint2bits(~(j / 2)) ⊦ j = ~1, j = 0, j % 2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ bits ≠ [] → (bits + bits0).rest = bits.rest + bits0

Rule argument

seq: ⊦ bits ≠ [] → (bits + bits0).rest = bits.rest + bits0 subst: [bits0, bits] → [true ', sgn(bitsinvert(uint2bits(~(j / 2))))] rotate: F spec: list inst: bitlista name: rest-01

Additional information

Used simplifier rules: uint2bits-empty: 0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ sgn(bits) = [] ↔ bits = [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];%j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0);% ⊦ 0 < j → (i / j ≤ 0 ↔ i < j);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ i ≤ ~ j ↔ i + j ≤ 0; Used terms: true ', sgn(bitsinvert(uint2bits(~(j / 2))))