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Proof step 53 from proof intshiftrsign-rec-pos (previous step)

# int2bits(i / 2) = m + 1, 0 < i, 1 < i, 0 ≤ i0, 0 ≤ i, i0 < 31 ⊦ bits2uint(sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ') = bits2int(sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 55:
¬ ( ¬ (sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ').first ∧ sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ' ≠ []), # int2bits(i / 2) = m + 1, 0 < i, 1 < i, 0 ≤ i0, 0 ≤ i, i0 < 31 ⊦ bits2uint(sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ') = bits2int(sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ')

Rule argument

seq: ⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits) subst: [bits] → [ sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] '] rotate: F spec: int2bits inst: name: bits2int-pos-02

Additional information

Used terms: sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] '