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Proof step 41 from proof reach-n-path-n (previous step)

1 + # x1 = 3 + n0, reachable-1(H, r0, r4), reachable-1(H, r4, r5), reachable-n(H, n0, r5, x1.last), path(r0 ' + x1, H), reachable-1(H, r, r0), reachable-1(H, r0, r2), reachable-1(H, r2, r3), reachable-n(H, n0, r3, x1.last) ⊦ x1 = [], r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ 2 + # x1 = 4 + n0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0
Proof step 43:
1 + # x1 = 3 + n0, reachable-1(H, r0, r4), reachable-1(H, r4, r5), reachable-n(H, n0, r5, x1.last), path(r0 ' + x1, H), r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0, reachable-1(H, r0, r2), reachable-1(H, r2, r3), reachable-n(H, n0, r3, x1.last) ⊦ x1 = [], r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ 2 + # x1 = 4 + n0

Rule argument

spec: inst: name: reachable-1-def seq: ⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0 subst: [r0, r, H] → [r0, r, H] flags: rewrite, current

Additional information

Used terms: r0, r, H