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Proof step 72 from proof hasSharing-dd-help (previous step)

(1 + # refs) + # refs1 = # refs2, # sks0 = 2 + # refs2 + # refs0, # refs4 = # refs0, st[r -- firstn(1 + # refs0, sks0)] = refval(r2), validrefs(str, (r2 ' + refs) + r1 ' + refs1 + r0 ', st[r2 -- _type] .type, st), validrefs(str, r ' + refs4 + (r2 ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st), fits(r, sks0, st), validrefs(str, r ' + refs0 + r2 ' + refs2 + r0 ', st[r -- _type] .type, st) ⊦ r2 = r1, r0 = jvmref, r1 = r0, path∃(str, r1, r2, st), path∃(str, r2, r1, st), hasSharing(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 66:
⊦ path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 71:
(1 + # refs) + # refs1 = # refs2, # sks0 = 2 + # refs2 + # refs0, # refs4 = # refs0, st[r -- firstn(1 + # refs0, sks0)] = refval(r2), validrefs(str, (r2 ' + refs) + r1 ' + refs1 + r0 ', st[r2 -- _type] .type, st), validrefs(str, r ' + refs4 + (r2 ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st), fits(r, sks0, st), validrefs(str, r ' + refs0 + r2 ' + refs2 + r0 ', st[r -- _type] .type, st) ⊦ r2 = r1, r0 = jvmref, r1 = r0, path∃(str, r1, r2, st), ∃ refs. refs ≠ [] ∧ refs .first = r2 ∧ refs .last = r1 ∧ validrefs(str, refs, st[r2 -- _type] .type, st), hasSharing(r, st)

Rule argument

[speclemmaarg: , path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st)) ,[st, r0, r, str] → [st, r1, r2, str] ,F ,cyclic , ,pathex-def-simple ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r1, r2, str)]]