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Proof step 8 from proof int2bits-len-neg (previous step)

j < 2 ^ i, j < 0, j < ~1, j + 2 ^ i < i, j + 2 ^ i < 0, 0 ≤ 2 ^ i * 2 + j, 0 ≤ i, 0 < 2 ^ i, j < i, j + 1 < 2 ^ i ⊦ # sgn(bitsinvert(uint2bits(~ j)) +1) = i→n(i + 2), true ∈ uint2bits(~ j).rest.rest

User applied rule insert lemma

And obtained the following new goals

Proof step 9:
1 < j ⊦ ∃ bits. uint2bits(j) = false ' + true ' + bits ∧ bits ≠ []
Proof step 10:
∃ bits. uint2bits(~ j) = false ' + true ' + bits ∧ bits ≠ [], j < 2 ^ i, j < 0, j < ~1, j + 2 ^ i < i, j + 2 ^ i < 0, 0 ≤ 2 ^ i * 2 + j, 0 ≤ i, 0 < 2 ^ i, j < i, j + 1 < 2 ^ i ⊦ # sgn(bitsinvert(uint2bits(~ j)) +1) = i→n(i + 2), true ∈ uint2bits(~ j).rest.rest

Rule argument

name: uint2bits-expos1 subst: [j] → [~ j]

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j = i0 → i < i0; (forward) Used terms: ~ j