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Proof step 643 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: junkrefs instance-name: lemma-name: validreflist-rec antecedent: succedent: validreflist(str, val ' + vals, ty, st) ↔ is_referencevalue(val) ∧ validref(str, val .refval, ty, st) ∧ validreflist(str, vals, ty, st) substlist: [st, ty, vals, val, str] → [st, mkclasstype(`java.lang.Object' .class), refval(r2) ', refval(r), str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 11)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : junkrefs, , validreflist-one-01, ⊦ validreflist (str, refval(r) ', ty, st) ↔ validref(str, r, ty, st)], [CSIMPNAMEDSEQ : junkrefs, , validref-object, ⊦ ¬ validref (str, r, mkclasstype (`java.lang.Object' .class), st) ∧ r ≠ jvmref → junkref(str, r, st)], [CSIMPNAMEDSEQ : junkrefs, , validref-object-01, ⊦ ¬ validref (str, r, mkclasstype (`java.lang.Object' .class), st) ∧ r ≠ jvmref → ¬ validref(str, r, ty, st)])], [EXTRATERMS : (st, mkclasstype(`java.lang.Object' .class), refval(r2) ', refval(r), str)]]