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Proof step 555 from proof hasSharing-put-index-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- sks0]) = refval(r1), (st[r0 -- i ', refval(r2)][r3 -- i ']) = refval(r4), (st[r0 -- i ', refval(r2)][r -- sks1]) = refval(r3), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r4 -- sks3]) = refval(r1), fits(r4, sks3, st[r0 -- i ', refval(r2)]), fits(r, sks1, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r, sks0, st[r0 -- i ', refval(r2)]), is_referencevalue(st[r0 -- i ', refval(r2)][r3 -- (i ' ' + sks3)]), is_arraytype(st[r3 -- _type] .type) → 0 ≤ i ∧ i < st[r3 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r3 = jvmref, r0 = jvmref, r = r2, r1 = jvmref, sks0 = [], sks0 = sks1 + i ' ' + sks3, sks1 = [], is_classtype(st[r3 -- _type] .type), junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks, sks2. sks1 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-put-other antecedent: succedent: ¬ (∃ sks0, sks1. sks = sks0 + (sk + sks1) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + sk ⊑ sks0 → st[r -- sks2] .refval ≠ r0)) → (st[r0 -- sk, val][r -- sks]) = st[r -- sks] substlist: [sks, r, val, sk, r0, st] → [sks1, r, refval(r2), i ', r0, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 3, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks1, r, refval(r2), i ', r0, st)]]