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Proof step 59 from proof bor-2pot-plus (previous step)

int2bits(j0) = false ' + bitsinvert(bits), 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j, false ∈ int2bits(j0), # int2bits(j0) ≤ i→n(i) ⊦ bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], 2 ^ n→i(# fillsgn(i→n(i), bitsinvert(int2bits(j0)))) * j + bits2uint(bitsinvert(fillsgn(i→n(i), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0, fillsgn(i→n(i), bitsinvert(int2bits(j0))) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → bitsinvert(fillsgn(n, bits)) = fillsgn(n, bitsinvert(bits)) subst: [bits, n] → [bitsinvert(int2bits(j0)), i→n(i)] rotate: F spec: bitopsaux inst: name: inv-fill

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: bitsinvert(int2bits(j0)), i→n(i)