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Proof step 763 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[r2 -- sks2] = refval(r1), 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, sks2, st) ⊦ sks1 = [], sks1 + i ' ' + sks2 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, sks2 = [], r2 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), validreflist(str, refval(r) ' + refval(r2) ', mkclasstype(`java.lang.Object' .class), st), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks1 = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks0, sks3. sks2 = sks0 + i ' ' + sks3 ∧ st[r2 -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r2 -- sks4] .refval ≠ st[r2 -- sks0] .refval)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 758:
⊦ validreflist(str, val ' + vals, ty, st) ↔ is_referencevalue(val) ∧ validref(str, val .refval, ty, st) ∧ validreflist(str, vals, ty, st)
Proof step 762:
st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r0), st[r2 -- sks2] = refval(r1), 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, sks2, st) ⊦ sks1 = [], sks1 + i ' ' + sks2 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, sks2 = [], r2 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), is_referencevalue(refval(r)) ∧ validref(str, refval(r) .refval, mkclasstype(`java.lang.Object' .class), st) ∧ validreflist(str, refval(r2) ', mkclasstype(`java.lang.Object' .class), st), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks1 = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks0, sks3. sks2 = sks0 + i ' ' + sks3 ∧ st[r2 -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r2 -- sks4] .refval ≠ st[r2 -- sks0] .refval)

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 : ()], [EXTRATERMS : (st, mkclasstype(`java.lang.Object' .class), refval(r2) ', refval(r), str)]]