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Proof step 223 from proof hasSharing-put-index-refval (previous step)

(st[r -- i ', refval(r2)][r2 -- sks3]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]) = refval(r1), 0 < st[r -- _length] .intval, fits(r2, sks1, st[r -- i ', refval(r2)]), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks3, st[r -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st) ⊦ r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks3 = [], sks1 = sks3, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 123:
⊦ is_referencevalue(st[r -- sks]) ∧ sks ≠ [] → st[r -- sks] = st[st[r -- sks .first] .refval -- sks .rest]
Proof step 222:
is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]) ∧ i ' ' + sks1 ≠ [], (st[r -- i ', refval(r2)][r2 -- sks3]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][(st[r -- i ', refval(r2)][r -- (i ' ' + sks1) .first]) .refval -- (i ' ' + sks1) .rest]) = refval(r1), 0 < st[r -- _length] .intval, fits(r2, sks1, st[r -- i ', refval(r2)]), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks3, st[r -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st) ⊦ r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks3 = [], sks1 = sks3, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st)

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 ' ' + sks1, r, 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 : javavalue, , test-19, ⊦ is_referencevalue(refval(r))])], [EXTRATERMS : (i ' ' + sks1, r, st[r -- i ', refval(r2)])]]