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Proof step 1 from proof reach-n-split-le (conclusion)

reachable-n(H, n, r, r0), m ≤ n ⊦ ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0)

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
reachable-n(H, n, r, r0), m < n ⊦ ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0)

Rule argument

spec: inst: name: reach-n-split seq: reachable-n(H, n, r, r0), m < n ⊦ ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0) subst: [H, n, r, r0, m] → [H, n, r, r0, m] flags: current, []

Additional information

Used simplifier rules: reachable-n-base: ⊦ reachable-n(H, 0, r, r0) ↔ r = r0;%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat%ler: ⊦ m ≤ m; from specification nat%zero: ⊦ m - m = 0; from specification nat Used terms: H, n, r, r0, m