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Proof step 61 from proof cast-help-comm (previous step)

# int2bits(j) < i→n(i0), # int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0, ¬ 0 ≤ j → j < 0 ⊦ bits2int(restn(i→n(i0) - i→n(i), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j))) = j, i→n(i0) = # int2bits(j), mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 62:
⊦ n ≤ # bits → restn(n, bits + bits0) = restn(n, bits) + bits0
Proof step 63:
¬ i→n(i0) - i→n(i) ≤ # mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)), # int2bits(j) < i→n(i0), # int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0, ¬ 0 ≤ j → j < 0 ⊦ bits2int(restn(i→n(i0) - i→n(i), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)) + int2bits(j))) = j, i→n(i0) = # int2bits(j), mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0
Proof step 65:
i→n(i0) - i→n(i) ≤ # mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)), # int2bits(j) < i→n(i0), # int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0, ¬ 0 ≤ j → j < 0 ⊦ bits2int(restn(i→n(i0) - i→n(i), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j))) + int2bits(j)) = j, i→n(i0) = # int2bits(j), mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0

Rule argument

seq: ⊦ n ≤ # bits → restn(n, bits + bits0) = restn(n, bits) + bits0 subst: [bits0, bits, n] → [int2bits(j), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)), i→n(i0) - i→n(i)] rotate: F spec: list-del inst: bitlista name: restN-append

Additional information

Used terms: int2bits(j), mklist(¬ 0 ≤ j, i→n(i0) - # int2bits(j)), i→n(i0) - i→n(i)