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Proof step 20 from proof uint2bits-2potrec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 22:
¬ i→n(i) + 1 ≤ #(false ' + lastn(i→n(i), uint2bits(j))), i→n(i) < # uint2bits(j), i→n(i) + 1 < # uint2bits(j), 2 ^ i ≤ j, 0 ≤ i, 2 ^ i < j, # lastn(i→n(i), uint2bits(j)) ≤ i→n(i), # lastn(i→n(i), uint2bits(j)) < # uint2bits(j) ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + fillsgn(i→n(i) + 1, false ' + lastn(i→n(i), uint2bits(j))).rest
Proof step 25:
i→n(i) + 1 ≤ #(false ' + lastn(i→n(i), uint2bits(j))), i→n(i) < # uint2bits(j), i→n(i) + 1 < # uint2bits(j), 2 ^ i ≤ j, 0 ≤ i, 2 ^ i < j, # lastn(i→n(i), uint2bits(j)) ≤ i→n(i), # lastn(i→n(i), uint2bits(j)) < # uint2bits(j) ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + (false ' + lastn(i→n(i), uint2bits(j))).rest

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [false ' + lastn(i→n(i), uint2bits(j)), i→n(i) + 1] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: false ' + lastn(i→n(i), uint2bits(j)), i→n(i) + 1