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Proof step 3 from proof pot-nls (previous step)

i ^ j < i ^ 1, i ^ j < i, 0 < i, 0 < j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: ls-pos seq: ⊦ 1 < i ∧ 0 ≤ j → (i ^ j < i ^ j0 ↔ j < j0) subst: [j0, j, i] → [1, j, i] flags: rewrite, current

Additional information

Used simplifier rules: one: ⊦ i ^ 1 = i;%pot-lez: ⊦ 0 < i → (i ^ j ≤ 0 ↔ i ^ j = 0);%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i);%bet-01: ⊦ 0 ≤ i → (i < 1 ↔ i = 0); from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs Used terms: 1, j, i