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Proof step 3 from proof lemon2pot-02 (previous step)

2 ^ n→i(m * n0 - 1) + j0 < j, 2 ^ n→i(m * n0 - 1) < 2 ^ n→i(m * n - 1), j ≤ 2 ^ n→i(m * n - 1) + j0, n ≤ n0 ⊦ m = 0, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 1 < i ∧ 0 ≤ j → (i ^ j < i ^ j0 ↔ j < j0)
Proof step 5:
n→i(m * n0 - 1) < n→i(m * n - 1), 2 ^ n→i(m * n0 - 1) + j0 < j, 1 < 2, n ≤ n0, j ≤ 2 ^ n→i(m * n - 1) + j0, 0 ≤ n→i(m * n0 - 1) ⊦ m = 0, n = 0

Rule argument

spec: <toplevel> name: ls-pos seq: ⊦ 1 < i ∧ 0 ≤ j → (i ^ j < i ^ j0 ↔ j < j0) subst: [j0, j, i] → [n→i(m * n - 1), n→i(m * n0 - 1), 2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n); (s) Used terms: n→i(m * n - 1), n→i(m * n0 - 1), 2