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Proof step 27 from proof cast-mod-pos-high (previous step)

# int2bits(j) = i→n(i) + 1, 0 < j, j < 2 ^ i, 0 ≤ 2 ^ (i - 1) + j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 ≤ i, 0 < i ⊦ 2 ^ i + j = j % 2 ^ i + 2 ^ (n→i(# uint2bits(j)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 29:
0 ≤ j, # int2bits(j) = i→n(i) + 1, 0 < j, j < 2 ^ i, 0 ≤ 2 ^ (i - 1) + j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 ≤ i, 0 < i ⊦ 2 ^ i + j = j % 2 ^ i + 2 ^ (n→i(# int2bits(j)) - 1)

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [j] rotate: T spec: int2bits inst: name: int2bits-pos

Additional information

Used terms: j