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Proof step 20 from proof path-dups (previous step)

(r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1 ⊦ x1 = [], m = 0, reachable-n(H, m, r, r)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 3:
⊦ n ≠ 0 → (reachable-n(H, n, r, r0) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x .last = r0 ∧ # x = n + 1))
Proof step 19:
m ≠ 0 → (reachable-n(H, m, r, r) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x .last = r ∧ # x = m + 1)), (r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1 ⊦ x1 = [], m = 0, reachable-n(H, m, r, r)

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reach-n-path-n antecedent: succedent: n ≠ 0 → ( reachable-n(H, n, r, r0) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x .last = r0 ∧ # x = n + 1)) substlist: [n, H, r, r0] → [m, H, r, r] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (m, H, r, r)]]