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Proof step 744 from proof hasSharing-put-index-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r2 -- sks0] = refval(r0), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r2, sks0 + i ' ' + sks3, st[r0 -- i ', refval(r2)]) ⊦ sks1 = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, r2 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r2 -- sks4] .refval ≠ r0)

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[r0 -- i ', refval(r2)], i ' ' + sks3, sks0, r2] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 12)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- i ', refval(r2)], i ' ' + sks3, sks0, r2)]]