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Proof step 117 from proof uint2bits-add-high (previous step)

uint2bits(2 ^ (i - 1) + i1 - 1) = sgn(int2bits(i1 - 1).rest), 2 ^ (i - 1) + i1 * 2 < i, abs(i1 - 1) ≤ 2 ^ (i - 1), 2 ^ (i - 2) < abs(i1 - 1), abs(i1 - 1) < 2 ^ i, 0 ≤ i, 1 < i, 0 < i, 1 < 2 ^ i + i1 * 2, 0 < 2 ^ i + i1 * 2, i1 * 2 + 2 ^ (i - 1) ≤ 0, 0 ≤ 2 ^ i, i1 < 0, ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ 2 ^ (i0 - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i0 → uint2bits(j + 2 ^ i0) = sgn(int2bits(j).rest) ⊦ i = 1, i1 = 0, 2 ^ i + i1 * 2 = 2, sgn(int2bits(i1 - 1).rest) + true ' = sgn(int2bits(i1 - 1).rest + true '), false ∈ int2bits(i1 - 1).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 118:
⊦ i < ~1 → false ∈ int2bits(i).rest

Rule argument

name: int2bits-falsein-01 rotate: F subst: [i] → [i1 - 1]

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < 0 ∧ 0 ≤ j → i < j; Used terms: i1 - 1