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Proof step 18 from proof intshiftrsign32 (previous step)

32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n0, fillsgn(32, int2bits(i)))), band(j, 31) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 20:
# int2bits(i) ≤ 32 ∧ int2bits(i) ≠ [], 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n0, mklist(int2bits(i).first, 32 - # int2bits(i)) + int2bits(i))), band(j, 31) = 0

Rule argument

spec: bitopsaux inst: name: fill-fill seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [int2bits(i), 32] flags: rewrite

Additional information

Used simplifier rules: int2bits-not-empty: ⊦ int2bits(j) ≠ []; from specification int2bits Used terms: int2bits(i), 32