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Proof step 81 from proof shiftright-rec-pos (previous step)

0 ≤ i, 0 ≤ i0, 1 < i, 0 < i, firstn(# int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2)).first ⊦ bits2uint(firstn(# int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2))) = bits2int(firstn(# int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first) subst: [bits, n] → [mklist(false, i→n(i0)) + int2bits(i / 2), # int2bits(i / 2)] rotate: F spec: list-del inst: bitlista name: firstn-first

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ ¬ 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(i0)) + int2bits(i / 2), # int2bits(i / 2)