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Proof step 10 from proof path-dups (previous step)

m0 < # x1, path(x1[m0] ' + x1, H) ⊦ x1 = [], path(x1[m0] ' + firstn(m0 + 1, x1), H), reachable-n(H, m0 + 1, x1[m0], x1[m0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ path(r ' + x + y, H) → (¬ path(r ' + x, H) ↔ false)
Proof step 9:
¬ path(x1[m0] ' + firstn(m0 + 1, x1) + restn(m0 + 1, x1), H), m0 < # x1, path(x1[m0] ' + x1, H) ⊦ x1 = [], path(x1[m0] ' + firstn(m0 + 1, x1), H), reachable-n(H, m0 + 1, x1[m0], x1[m0])

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: path-prefix antecedent: succedent: path(r ' + x + y, H) → (¬ path(r ' + x, H) ↔ false) substlist: [y, H, x, r] → [restn(m0 + 1, x1), H, firstn(m0 + 1, x1), x1[m0]] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (restn(m0 + 1, x1), H, firstn(m0 + 1, x1), x1[m0])]]