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Proof step 12 from proof shiftzero-max-neg-01 (previous step)

# int2bits(~1) ≤ n, j ≤ n→i(n), 2 ^ (n→i(n) - j) ≤ >>>(n, ~1, j), 0 < j, ∀ n, i, j0. i→n(j0) < i→n(j) → 0 < j0 ∧ i < 0 ∧ 2 ^ (n→i(n) - j0) ≤ >>>(n, i, j0) ∧ j0 ≤ n→i(n) ∧ # int2bits(i) ≤ n → n = 0 ⊦ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ i + 1 = 0 → int2bits(i) = true '
Proof step 14:
~1 + 1 = 0, # true ' ≤ n, j ≤ n→i(n), 2 ^ (n→i(n) - j) ≤ >>>(n, ~1, j), 0 < j, ∀ n, i, j0. i→n(j0) < i→n(j) → 0 < j0 ∧ i < 0 ∧ 2 ^ (n→i(n) - j0) ≤ >>>(n, i, j0) ∧ j0 ≤ n→i(n) ∧ # int2bits(i) ≤ n → n = 0 ⊦ n = 0

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