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Proof step 80 from proof cast-mod-neg-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 81:
⊦ i + 1 = 0 → int2bits(i) = true '
Proof step 82:
~1 + 1 = 0, ~1 = j % 2 ^ i, i→n(i) = # fillsgn(i→n(i) + 1, true ').rest, # true ' ≤ i→n(i), j + 2 ^ i < i, j + 2 ^ i ≤ 0, j < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, j + 2 ^ i < 2 ^ (i - 1), 0 < i, j + 1 < 2 ^ (i - 1), j < ~1 ⊦ bits2int(fillsgn(i→n(i) + 1, true ').rest) = ~1, j = ~1, i = 1

Rule argument

seq: ⊦ i + 1 = 0 → int2bits(i) = true ' subst: [i] → [~1] rotate: F spec: int2bits inst: name: int2bits-mone

Additional information

Used terms: ~1