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Proof step 9 from proof ls-pos-02 (previous step)

i0 ^ (i1 + 1) < i ^ (i1 + 1), i ≤ i0, 0 ≤ i0, 0 ≤ i, ~1 ≤ i1, ∀ j0, i0, i. i→n(j0) < i→n(i1 + 1) → i0 ^ j0 < i ^ j0 ∧ i ≤ i0 ∧ 0 ≤ j0 ∧ 0 ≤ i ∧ 0 ≤ i0 → false ⊦ i0 ^ i1 < i ^ i1 ∧ 0 ≤ i1

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 0 ≤ i1

Additional information

Used simplifier rules: Pot-neg: ⊦ i < 0 → j ^ i = 1 / j ^ abs(i);%Pot-zero: ⊦ j ^ 0 = 1;% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); (s)% ⊦ i < 0 → abs(i) = ~ i; (s)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: 0 ≤ i1