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Proof step 198 from proof hasSharing-put-index-refval (previous step)

(st[r -- i ', refval(r2)][r2 -- (sks + i ' ' + sks0)]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), st[r2 -- sks1] = refval(r1), st[r2 -- sks] = refval(r), 0 < st[r -- _length] .intval, is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]), fits(r2, sks1, st), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks + i ' ' + sks0, st[r -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st) ⊦ r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks1 = sks + i ' ' + sks0, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks2, sks0. sks1 = sks2 + i ' ' + sks0 ∧ st[r2 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ st[r2 -- sks2] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-append antecedent: succedent: fits(r, sks + sks0, st) ↔ fits(r, sks, st) ∧ fits(st[r -- sks] .refval, sks0, st) substlist: [st, sks0, sks, r] → [st[r -- i ', refval(r2)], i ' ' + sks0, sks, r2] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 9)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- i ', refval(r2)], i ' ' + sks0, sks, r2)]]