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Proof step 14 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 ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + fillsgn(i→n(i) + 1, sgn(false ' + lastn(i→n(i), uint2bits(j)))).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ # bits ≤ n → fillsgn(n, sgn(bits)) = fillsgn(n, bits)
Proof step 16:
¬ #(false ' + lastn(i→n(i), uint2bits(j))) ≤ i→n(i) + 1, 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
Proof step 19:
#(false ' + lastn(i→n(i), uint2bits(j))) ≤ i→n(i) + 1, 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, false ' + lastn(i→n(i), uint2bits(j))).rest

Rule argument

seq: ⊦ # bits ≤ n → fillsgn(n, sgn(bits)) = fillsgn(n, bits) subst: [bits, n] → [false ' + lastn(i→n(i), uint2bits(j)), i→n(i) + 1] rotate: F spec: bitopsaux inst: name: fill-sgn-01

Additional information

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