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Proof step 8 from proof shiftright-neg-mone (previous step)

0 ≤ 2 ^ (abs(j) - 1) + i, i < 0 ⊦ bits2int(firstn(# int2bits(i), mklist(true, i→n(j)) + int2bits(i))) = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ m ≤ # bits → firstn(m, bits + bits0) = firstn(m, bits)
Proof step 10:
¬ # int2bits(i) ≤ # mklist(true, i→n(j)), 0 ≤ 2 ^ (abs(j) - 1) + i, i < 0 ⊦ bits2int(firstn(# int2bits(i), mklist(true, i→n(j)) + int2bits(i))) = ~1

Rule argument

seq: ⊦ m ≤ # bits → firstn(m, bits + bits0) = firstn(m, bits) subst: [bits0, bits, m] → [int2bits(i), mklist(true, i→n(j)), # int2bits(i)] rotate: F spec: list-del inst: bitlista name: first-append

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ m ≤ n → firstn(m, mklist(boolvar, n)) = mklist(boolvar, m);% ⊦ bits2int(mklist(true, # int2bits(i))) = ~1; Used terms: int2bits(i), mklist(true, i→n(j)), # int2bits(i)