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Proof step 49 from proof reach-n-path-n (previous step)

1 + # x1 = 3 + n, path(r ' + x1, H), ∀ H0, r1, r2. (∃ r3. reachable-1(H0, r1, r3) ∧ reachable-n(H0, n, r3, r2)) ↔ (∃ x. path(x, H0) ∧ hd x = r1 ∧ x.last = r2 ∧ # x = 2 + n) ⊦ x1 = [], ∃ r0. reachable-1(H, r, r0) ∧ (∃ r1. reachable-1(H, r0, r1) ∧ reachable-n(H, n, r1, (r ' + x1).last))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
1 + # x1 = 3 + n, path(r ' + x1, H), ∀ H0, r1, r2. (∃ r3. reachable-1(H0, r1, r3) ∧ reachable-n(H0, n, r3, r2)) ↔ (∃ x. path(x, H0) ∧ hd x = r1 ∧ x.last = r2 ∧ # x = 2 + n) ⊦ x1 = [], ∃ r0. reachable-1(H, r, r0) ∧ (∃ r1. reachable-1(H, r0, r1) ∧ reachable-n(H, n, r1, x1.last))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-02: ⊦ x0 ≠ [] → (r ' + x0).last = x0.last; from specification list-last[reflist]