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Proof step 660 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 618:
⊦ sks ≠ [] ∧ sks0 ≠ [] → st[r -- (sks + sks0)] = st[st[r -- sks] .refval -- sks0]
Proof step 659:
sks0 ≠ [] ∧ i ' ' + sks1 ≠ [], st[r -- sks] = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][(st[r -- i ', refval(r2)][r2 -- sks0]) .refval -- (i ' ' + sks1)]) = refval(r1), st[r2 -- sks0] = refval(r), 0 < st[r -- _length] .intval, fits(r2, sks0 + i ' ' + sks1, st[r -- i ', refval(r2)]), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r -- _length] .intval, 0 ≤ i ⊦ i ' ' + sks0 + i ' ' + sks1 = sks, r = jvmref, r = r2, r1 = jvmref, sks = [], r2 = jvmref, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks0 → st[r2 -- sks3] .refval ≠ r)

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-append antecedent: succedent: sks ≠ [] ∧ sks0 ≠ [] → st[r -- (sks + sks0)] = st[st[r -- sks] .refval -- sks0] substlist: [sks0, sks, r, st] → [i ' ' + sks1, sks0, r2, st[r -- i ', refval(r2)]] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2, 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 : storefuns, , lookup-empty, ⊦ st[r -- []] = refval(r)], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0])], [EXTRATERMS : (i ' ' + sks1, sks0, r2, st[r -- i ', refval(r2)])]]