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Proof step 20 from proof intshiftright-ls-01 (previous step)

# int2bits(i) = m + 1, mklist(i < 0, i→n(j)) + int2bits(i) = true ' + bits, j < 32, 0 ≤ j ⊦ bits2int(true ' + sublist(0, m, bits)) < 0 ↔ ¬ 0 < i, mklist(¬ 0 < i, i→n(j)) + int2bits(i) = [], i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ bits2int(true ' + bits) = ~ bits2uint(bitsinvert(true + bits) +1)
Proof step 22:
# int2bits(i) = m + 1, mklist(i < 0, i→n(j)) + int2bits(i) = true ' + bits, j < 32, 0 ≤ j ⊦ ~ bits2uint(bitsinvert(true + sublist(0, m, bits)) +1) < 0 ↔ ¬ 0 < i, mklist(¬ 0 < i, i→n(j)) + int2bits(i) = [], i = 0

Rule argument

seq: ⊦ bits2int(true ' + bits) = ~ bits2uint(bitsinvert(true + bits) +1) subst: [bits] → [sublist(0, m, bits)] rotate: F spec: int2bits inst: name: bits2int-neg

Additional information

Used terms: sublist(0, m, bits)