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Proof step 25 from proof shiftzero-minus-one (previous step)

firstn(n, mklist(false, i→n(j)) + mklist(true, n)).first ⊦ n = 0, j = 0, bits2int(firstn(n, mklist(false, i→n(j)) + mklist(true, n))) = bits2uint(firstn(n, mklist(false, i→n(j)) + mklist(true, n)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first)
Proof step 27:
n ≠ 0 ∧ mklist(false, i→n(j)) + mklist(true, n) ≠ [], (mklist(false, i→n(j)) + mklist(true, n)).first ⊦ n = 0, j = 0, bits2int(firstn(n, mklist(false, i→n(j)) + mklist(true, n))) = bits2uint(firstn(n, mklist(false, i→n(j)) + mklist(true, n)))

Rule argument

seq: ⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first) subst: [bits, n] → [mklist(false, i→n(j)) + mklist(true, n), n] rotate: F spec: list-del inst: bitlista name: firstn-first

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: mklist(false, i→n(j)) + mklist(true, n), n