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Proof step 4 from proof bint-unsigned-01 (previous step)

0 ≤ i, 0 < i, i < 4294967296, 2147483648 ≤ i ⊦ i = cast(32, i) + 4294967296

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < i → cast(i, j) = (0 ≤ j ∧ j % 2 ^ i ≤ 2 ^ (i - 1) - 1 ⊃ j % 2 ^ i ;(0 ≤ j ∧ 2 ^ (i - 1) - 1 < j % 2 ^ i ⊃ j % 2 ^ i - 2 ^ i ;(j < 0 ∧ j % 2 ^ i < ~(2 ^ (i - 1)) ⊃ j % 2 ^ i + 2 ^ i;(j < 0 ∧ ~(2 ^ (i - 1)) ≤ j % 2 ^ i ⊃ j % 2 ^ i;j)) ) )

Rule argument

seq: ⊦ 0 < i → cast(i, j) = (0 ≤ j ∧ j % 2 ^ i ≤ 2 ^ (i - 1) - 1 ⊃ j % 2 ^ i ;(0 ≤ j ∧ 2 ^ (i - 1) - 1 < j % 2 ^ i ⊃ j % 2 ^ i - 2 ^ i ;(j < 0 ∧ j % 2 ^ i < ~(2 ^ (i - 1)) ⊃ j % 2 ^ i + 2 ^ i ;(j < 0 ∧ ~(2 ^ (i - 1)) ≤ j % 2 ^ i ⊃ j % 2 ^ i;j) ) ) ) subst: [j, i] → [i, 32] rotate: F spec: intops inst: name: cast-if

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%0 < j ⊦ 0 ≤ i ∧ i < j → i % (* j) = i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;%i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j;% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i, 32