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Proof step 8 from proof int2bits-restsgn (previous step)

0 ≤ j, j ≤ 2 ^ n→i(# int2bits(j)), 0 ≤ 2 ^ n→i(# int2bits(j)) ⊦ sgn(uint2bits(2 ^ n→i(# int2bits(j)) - j).rest) = uint2bits(2 ^ n→i(# int2bits(j)) - j).rest, ∃ i. 2 ^ i = j

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 9:
⊦ 0 < j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1))
Proof step 10:
0 < j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1)), 0 ≤ j, j ≤ 2 ^ n→i(# int2bits(j)), 0 ≤ 2 ^ n→i(# int2bits(j)) ⊦ sgn(uint2bits(2 ^ n→i(# int2bits(j)) - j).rest) = uint2bits(2 ^ n→i(# int2bits(j)) - j).rest, ∃ i. 2 ^ i = j

Rule argument

seq: ⊦ 0 < j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1)) subst: [j] → [j] rotate: F spec: int-pot inst: name: exin2pot

Additional information

Used terms: j