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Proof step 557 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 313:
⊦ is_referencevalue(st[r -- sks]) ∧ sks ≠ [] → st[r -- sks] = st[st[r -- sks .first] .refval -- sks .rest]
Proof step 556:
is_referencevalue(st[r0 -- i ', refval(r2)][r3 -- (i ' ' + sks3)]) ∧ i ' ' + sks3 ≠ [], st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r -- sks1]) = refval(r3), (st[r0 -- i ', refval(r2)][r3 -- i ']) = refval(r4), (st[r0 -- i ', refval(r2)][r -- sks0]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][(st[r0 -- i ', refval(r2)][r3 -- (i ' ' + sks3) .first]) .refval -- (i ' ' + sks3) .rest]) = refval(r1), fits(r, sks0, st[r0 -- i ', refval(r2)]), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks1, st), fits(r4, sks3, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty), is_arraytype(st[r3 -- _type] .type) → 0 ≤ i ∧ i < st[r3 -- _length] .intval ⊦ sks1 = [], sks0 = sks1 + i ' ' + sks3, sks0 = [], r1 = jvmref, r = r2, r0 = jvmref, r3 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), is_classtype(st[r3 -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0), ∃ sks, sks2. sks1 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval)

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-rec-refval antecedent: succedent: is_referencevalue(st[r -- sks]) ∧ sks ≠ [] → st[r -- sks] = st[st[r -- sks .first] .refval -- sks .rest] substlist: [sks, r, st] → [i ' ' + sks3, r3, st[r0 -- i ', refval(r2)]] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 5, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, app-02-ant, ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))])], [EXTRATERMS : (i ' ' + sks3, r3, st[r0 -- i ', refval(r2)])]]