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Proof step 12 from proof intshiftrsign32 (previous step)

band(j, 31) = 0, # int2bits(i) ≤ 32 ⊦ i = bits2int(sublist(0, 32, fillsgn(32, int2bits(i))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ # bits = n → sublist(0, n, bits) = bits
Proof step 14:
# fillsgn(32, int2bits(i)) = 32, band(j, 31) = 0, # int2bits(i) ≤ 32 ⊦ i = bits2int(fillsgn(32, int2bits(i)))

Rule argument

spec: list-del inst: bitlista name: sublist-all seq: ⊦ # bits = n → sublist(0, n, bits) = bits subst: [bits, n] → [fillsgn(32, int2bits(i)), 32] flags: rewrite

Additional information

Used simplifier rules: fill-length: ⊦ # bits ≤ n → # fillsgn(n, bits) = n; from specification bitopsaux Used terms: fillsgn(32, int2bits(i)), 32