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Proof step 56 from proof shiftzero-pos (previous step)

# int2bits(i) = i→n(j), 0 ≤ i, i→n(j) < n ⊦ bits2int(firstn(n, mklist(false, n) + int2bits(i))) = 0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ m ≤ # bits → firstn(m, bits + bits0) = firstn(m, bits)
Proof step 58:
n ≤ # mklist(false, n), # int2bits(i) = i→n(j), 0 ≤ i, i→n(j) < n ⊦ bits2int(firstn(n, mklist(false, n))) = 0, j = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ n < n; Used terms: int2bits(i), mklist(false, n), n