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Proof step 172 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 171:
st[r2 -- sks3] = refval(r) ∧ is_referencevalue(st[r2 -- sks3]), (st[r -- i ', refval(r2)][r2 -- (sks3 + i ' ' + sks4)]) = refval(r0), st[r2 -- (sks3 + i ' ' + sks4)] = refval(r), st[r2 -- sks1] = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r2 -- ((sks3 + i ' ' + sks4) + i ' ' + sks0)]) = refval(r1), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r0, i ' ' + sks0, st[r -- i ', refval(r2)]), fits(r2, sks3 + i ' ' + sks4, st[r -- i ', refval(r2)]), 0 ≤ i, i < st[r -- _length] .intval, fits(r2, sks1, st), is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]), 0 < st[r -- _length] .intval ⊦ sks1 = (sks3 + i ' ' + sks4) + i ' ' + sks0, r2 = jvmref, r1 = jvmref, r = r2, r = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks3 → st[r2 -- sks2] .refval ≠ r), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks3 + i ' ' + sks4 → st[r2 -- sks2] .refval ≠ r), ∃ sks2, sks0. sks1 = sks2 + i ' ' + sks0 ∧ st[r2 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ st[r2 -- sks2] .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 -- sks3], 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], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r2 -- sks3], r)]]