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Proof step 23 from proof uint2bits-2potrec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ 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; Used terms: uint2bits(j), i→n(i)