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Proof step 33 from proof intshiftrsign-rec-neg (previous step)

0 + # int2bits((i - 1) / 2) ≤ #(mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)), i < 0, j < 32, 0 < j ⊦ j = 0, i = ~1, bits2int(true ' + sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2))) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j - 1)) + int2bits((i - 1) / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
bits ≠ [], ¬ (¬ bits.first) ∈ bits0 ⊦ bits2int(bits0 + bits) = bits2int(bits)
Proof step 35:
¬ ( sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)) ≠ [] ∧ ¬ (¬ sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)).first) ∈ true '), 0 + # int2bits((i - 1) / 2) ≤ #(mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)), i < 0, j < 32, 0 < j ⊦ j = 0, i = ~1, bits2int(true ' + sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2))) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j - 1)) + int2bits((i - 1) / 2)))
Proof step 41:
sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)) ≠ [] ∧ ¬ (¬ sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)).first) ∈ true ', 0 + # int2bits((i - 1) / 2) ≤ #(mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)), i < 0, j < 32, 0 < j ⊦ j = 0, i = ~1, bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2))) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j - 1)) + int2bits((i - 1) / 2)))

Rule argument

seq: bits ≠ [], ¬ (¬ bits.first) ∈ bits0 ⊦ bits2int(bits0 + bits) = bits2int(bits) subst: [bits, bits0] → [sublist (0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)), true '] rotate: F spec: int2bits inst: name: bits2int-sign

Additional information

Used terms: sublist (0, # int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)), true '