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Proof step 15 from proof cast-mod-pos-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ # bits = n + 1 → lastn(n, bits) = bits.rest
Proof step 17:
# int2bits(j) ≠ i→n(i) + 1, j < 2 ^ i, 0 ≤ 2 ^ (i - 1) + j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, 2 ^ (i - 1) ≤ j % 2 ^ i, i→n(i) ≤ # int2bits(j), 0 ≤ i ⊦ j % 2 ^ i = bits2int(lastn(i→n(i), int2bits(j))) + 2 ^ i
Proof step 23:
# int2bits(j) = i→n(i) + 1, j < 2 ^ i, 0 ≤ 2 ^ (i - 1) + j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, 2 ^ (i - 1) ≤ j % 2 ^ i, i→n(i) ≤ # int2bits(j), 0 ≤ i ⊦ j % 2 ^ i = bits2int(int2bits(j).rest) + 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)