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Proof step 8 from proof div-twopot (previous step)

i0 < 0, i0 < j, 0 < j, i0 + 1 < j, 0 ≤ j, 0 ≤ i0 + j ⊦ 2 ^ (i0 + j) / 2 ^ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div name: div-zero seq: 0 < j, 0 ≤ i, i < j ⊦ i / j = 0 subst: [j, i] → [2 ^ j, 2 ^ (i0 + j)] flags: <all paths>

Additional information

Used simplifier rules: two-lez: ⊦ 0 ≤ i → ¬ 2 ^ i ≤ 0;%two-lsz: ⊦ ¬ 2 ^ i < 0;%two-le: ⊦ 0 ≤ i → (2 ^ i ≤ 2 ^ j ↔ i ≤ j);% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i ≤ i + j ↔ 0 ≤ j; (s)% ⊦ i < j → (j ≤ i ↔ false); (as)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: 2 ^ j, 2 ^ (i0 + j)