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Proof step 2 from proof bint-succ-notin (previous step)

~2147483648 ≤ i, i ≤ 2147483647 ⊦ bi2i(i2bi(1 + i)) = ~2147483648, (i + 1)∈bint

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 2 ^ 31 ≤ i ∧ i < 2 ^ 32 → bi2i(i2bi(i)) = i - 2 ^ 32
Proof step 4:
¬(2 ^ 31 ≤ 1 + i ∧ 1 + i < 2 ^ 32), ~2147483648 ≤ i, i ≤ 2147483647 ⊦ bi2i(i2bi(1 + i)) = ~2147483648, (i + 1)∈bint

Rule argument

name: bint-unsigned-01 rotate: F subst: [i] → [1 + i]

Additional information

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