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Proof step 4 from proof reachable-n-rec-rev (previous step)

reachable-n(H, n + 1, r, r0) ⊦ ∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0), reachable-n(H, n + 1, r, r0) ∧ n < n + 1

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 2

Additional information

Used simplifier rules: reachable-n-rec: ⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, n, r1, r0));%reachable-1-def: ⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1