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Proof step 21 from proof divmod2-2pot-neg (previous step)

1 < i, i0 * 2 ^ i + j0 < 0, j0 < i, i0 < 0, 0 < i, j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i ⊦ ((j0 - 1) / 2) % 2 = ((j0 - 1) / 2 + i0 * 2 ^ (i - 1)) % 2, (i0 * 2 ^ (i - 1)) % 2 = 0, i0 = 0, j0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: mod-2pot seq: ⊦ 0 < i → (j * 2 ^ i) % 2 = 0 subst: [i, j] → [i - 1, i0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ i < j - i0 ↔ i + i0 < j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); (s)% ⊦ i = j → i - j = 0; (s)% ⊦ 1 * i = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ i < 0 → (~2 < i ↔ i = ~1); (s) Used terms: i - 1, i0