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Proof step 779 from proof hasSharing-put-index-refval (previous step)

st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r0, i ' ' + sks2, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ sks1 + i ' ' + sks2 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 595:
⊦ fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st)
Proof step 778:
st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st), r0 ≠ jvmref ∧ is_referencevalue(st[r0 -- i ', refval(r2)][r0 -- i ']) ∧ (is_classtype((st[r0 -- i ', refval(r2)][r0 -- _type]) .type) → i ' ∈ instfields((st[r0 -- i ', refval(r2)][r0 -- _type]) .type .class)) ∧ ( is_arraytype((st[r0 -- i ', refval(r2)][r0 -- _type]) .type) → is_indexkey(i ') ∧ 0 ≤ i ' .index ∧ i ' .index < (st[r0 -- i ', refval(r2)][r0 -- _length]) .intval) ∧ fits((st[r0 -- i ', refval(r2)][r0 -- i ']) .refval, sks2, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ sks1 + i ' ' + sks2 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, 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)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-storekeys-rec antecedent: succedent: fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ ( is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ ( is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st) substlist: [st, sks, sk, r] → [st[r0 -- i ', refval(r2)], sks2, i ', r0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 8)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- i ', refval(r2)], sks2, i ', r0)]]