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Proof step 67 from proof int2bytes-rec-neg-05 (previous step)

# int2bits(j) % 8 = 0, j < 0, 0 < 2 ^ (i * 8) + j, 0 < j + 2 ^ (i * 8), j + 2 ^ (i * 8 - 1) < 0, 0 < i ⊦ bits2bytes(int2bits(j)) = i2b(~1) ' + fix(i→n(i) + 1, bits2bytes(int2bits(j))).rest, j = 0, # bits2bytes(int2bits(j)) = i→n(i) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ # bits % 8 = 0 ∧ bits ≠ [] → # bits2bytes(bits) = # bits / 8
Proof step 69:
# int2bits(j) % 8 = 0 ∧ int2bits(j) ≠ [], # int2bits(j) % 8 = 0, j < 0, 0 < 2 ^ (i * 8) + j, 0 < j + 2 ^ (i * 8), j + 2 ^ (i * 8 - 1) < 0, 0 < i ⊦ bits2bytes(int2bits(j)) = i2b(~1) ' + fix(i→n(i) + 1, bits2bytes(int2bits(j))).rest, j = 0, # int2bits(j) / 8 = i→n(i) + 1

Rule argument

name: bits2bytes-len-01 rotate: F subst: [bits] → [int2bits(j)]

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ int2bits(j) ≠ []; Used terms: int2bits(j)