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Proof step 17 from proof uint2bits-2potrec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ n ≤ # bits → # lastn(n, bits) = n

Rule argument

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

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → m ≤ n;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 ≤ i → abs(i) = i;% ⊦ ¬ i < i; Used terms: uint2bits(j), i→n(i)