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Proof step 17 from proof int2bytes-fillsgn-rec (previous step)

# int2bytes(i >> 8) < n, 128 ≤ i, 0 ≤ i >> 8, 0 < i, 0 ≤ i, # int2bytes(i >> 8) + 1 < n ⊦ fillsgn(n, int2bytes(i >> 8) + i2b(i) ') = (mklist(i2b(0), n - 1 - # int2bytes(i >> 8)) + int2bytes(i >> 8)) + i2b(i) ', n = # int2bytes(i >> 8) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ # bytes < n ∧ 0 ≤ bytes2int(bytes) → fillsgn(n, bytes) = mklist(i2b(0), n - # bytes) + bytes
Proof step 19:
¬(#(int2bytes(i >> 8) + i2b(i) ') < n ∧ 0 ≤ bytes2int(int2bytes(i >> 8) + i2b(i) ')), # int2bytes(i >> 8) < n, 128 ≤ i, 0 ≤ i >> 8, 0 < i, 0 ≤ i, # int2bytes(i >> 8) + 1 < n ⊦ fillsgn(n, int2bytes(i >> 8) + i2b(i) ') = (mklist(i2b(0), n - 1 - # int2bytes(i >> 8)) + int2bytes(i >> 8)) + i2b(i) ', n = # int2bytes(i >> 8) + 1
Proof step 25:
#(int2bytes(i >> 8) + i2b(i) ') < n ∧ 0 ≤ bytes2int(int2bytes(i >> 8) + i2b(i) '), # int2bytes(i >> 8) < n, 128 ≤ i, 0 ≤ i >> 8, 0 < i, 0 ≤ i, # int2bytes(i >> 8) + 1 < n ⊦ mklist(i2b(0), n - #(int2bytes(i >> 8) + i2b(i) ')) + int2bytes(i >> 8) + i2b(i) ' = (mklist(i2b(0), n - 1 - # int2bytes(i >> 8)) + int2bytes(i >> 8)) + i2b(i) ', n = # int2bytes(i >> 8) + 1

Rule argument

name: fillsgn-pos rotate: F subst: [bytes, n] → [int2bytes(i >> 8) + i2b(i) ', n]

Additional information

Used terms: int2bytes(i >> 8) + i2b(i) ', n