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Proof step 12 from proof uint2bits-2potrec (previous step)

i→n(i) + 1 < # uint2bits(j), 2 ^ i ≤ j, 0 ≤ i, 2 ^ i < j ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + fillsgn(i→n(i) + 1, sgn(false ' + lastn(i→n(i), uint2bits(j).rest))).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ n < # bits → lastn(n, bits.rest) = lastn(n, bits)
Proof step 14:
i→n(i) < # uint2bits(j), i→n(i) + 1 < # uint2bits(j), 2 ^ i ≤ j, 0 ≤ i, 2 ^ i < j ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + fillsgn(i→n(i) + 1, sgn(false ' + lastn(i→n(i), uint2bits(j)))).rest

Rule argument

seq: ⊦ n < # bits → lastn(n, bits.rest) = lastn(n, bits) subst: [bits, n] → [uint2bits(j), i→n(i)] rotate: F spec: list-del inst: bitlista name: lastN-rest

Additional information

Used simplifier rules: ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: uint2bits(j), i→n(i)