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Proof step 164 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 163:
st[r2 -- sks0] = refval(r) ∧ is_referencevalue(st[r2 -- sks0]), (st[r -- i ', refval(r2)][r2 -- sks3]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r2 -- (sks0 + i ' ' + sks)]) = refval(r1), 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), is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks0 + i ' ' + sks)]), fits(r2, sks0 + i ' ' + sks, st), 0 < st[r -- _length] .intval, ∀ sks1. sks1 + i ' ' ⊑ sks0 → st[r2 -- sks1] .refval ≠ r ⊦ r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks3 = [], sks0 + i ' ' + sks = sks3, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks1, sks2. sks0 + i ' ' + sks = sks1 + i ' ' + sks2 ∧ st[r2 -- sks1] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks1 → st[r2 -- sks3] .refval ≠ st[r2 -- sks1] .refval)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-refval antecedent: is_referencevalue(val) succedent: r = val .refval ↔ val = refval(r) substlist: [val, r] → [st[r2 -- sks0], r] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : valuefuns, , refval-xtra, ⊦ ¬ is_referencevalue(val) → val .refval = jvmref], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r2 -- sks0], r)]]