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Proof step 112 from proof cast-mod-neg-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 113:
n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1
Proof step 114:
# int2bits(j % 2 ^ i) ≠ 0, # int2bits(j % 2 ^ i) = i→n(i) + 1, j % 2 ^ i < 0, 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i, j + 2 ^ i ≤ 0, j + 2 ^ i < i, i→n(i) < # int2bits(j % 2 ^ i), j % 2 ^ i < ~1 ⊦ 2 ^ (n→i(# int2bits(j % 2 ^ i)) - 1) = 0, j % 2 ^ i = 0, i = 1, j = ~1

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# int2bits(j % 2 ^ i), i→n(i)] rotate: F spec: nat inst: name: elim-pred-c

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: # int2bits(j % 2 ^ i), i→n(i)