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Proof step 32 from proof cast-mod-neg-high (previous step)

i→n(i) ≤ # int2bits(j), 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i, 0 < j + 2 ^ i ⊦ i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ # bits = n + 1 → lastn(n, bits) = bits.rest
Proof step 34:
# int2bits(j) ≠ i→n(i) + 1, i→n(i) ≤ # int2bits(j), 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i, 0 < j + 2 ^ i ⊦ i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i
Proof step 37:
# int2bits(j) = i→n(i) + 1, i→n(i) ≤ # int2bits(j), 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i, 0 < j + 2 ^ i ⊦ i = 1, j = ~1, bits2int(int2bits(j).rest) = j % 2 ^ i

Rule argument

seq: ⊦ # bits = n + 1 → lastn(n, bits) = bits.rest subst: [bits, n] → [int2bits(j), i→n(i)] rotate: F spec: list-del inst: bitlista name: lastN-rest-01

Additional information

Used terms: int2bits(j), i→n(i)