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Proof step 45 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
(st[r -- i ', refval(r2)][r0 -- i ']) = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r2 -- (sks + i ' ' + sks0)]) = refval(r2), st[r2 -- sks] = refval(r), (st[r -- i ', refval(r2)][r2 -- sks]) = refval(r0), 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, 0 ≤ i, disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r2, sks, st), is_referencevalue(st[r -- i ', refval(r2)][r0 -- i ']), fits(r1, sks0, st[r -- i ', refval(r2)]), is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval ⊦ r = jvmref, r = r2, r2 = jvmref, r0 = jvmref, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), is_classtype(st[r0 -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r2 -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r2 -- sks2] .refval ≠ st[r2 -- sks1] .refval)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-13 antecedent: succedent: is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) substlist: [val, r] → [st[r -- i ', refval(r2)][r0 -- i '], r1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- i ', refval(r2)][r0 -- i '], r1)]]