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Proof step 15 from proof le-pos-01 (previous step)

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

User applied rule cut formula

And closed the goal!

Rule argument

fma: i ^ i1 ≠ 0

Additional information

Used simplifier rules: Pot-zero: ⊦ j ^ 0 = 1;%Pot-zero: ⊦ j ^ 0 = 1;% ⊦ i * 0 = 0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 ≤ i → (0 ≤ i * j ↔ i = 0 ∨ 0 ≤ j); (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s) Used formulas: i ^ i1 ≠ 0