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Proof step 48 from proof path-dups (previous step)

(r ' + x1)[# x2] = x1[m0], x1[m0] = x2 .last, path(r ' + x1, H), path(r ' + x2, H), reachable-n(H, # x2, r, x1[m0]), # x2 < # x1, m0 < # x1, # x2 ≤ m0 ⊦ x1 = [], x2 = [], path(r ' + firstn(m0 + 1, x1), H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ path(r ' + x + y, H) → (¬ path(r ' + x, H) ↔ false)
Proof step 47:
¬ path(r ' + firstn(m0 + 1, x1) + restn(m0 + 1, x1), H), (r ' + x1)[# x2] = x1[m0], x1[m0] = x2 .last, path(r ' + x1, H), path(r ' + x2, H), reachable-n(H, # x2, r, x1[m0]), # x2 < # x1, m0 < # x1, # x2 ≤ m0 ⊦ x1 = [], x2 = [], path(r ' + firstn(m0 + 1, x1), H)

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), r] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 2)) dummy: () ]

Additional information

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