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Proof step 228 from proof hasSharing-put-index-refval (previous step)

(st[r0 -- i ', refval(r4)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r4)][r0 -- sks]) = refval(r), validref(str, r4, ty, st), disjoint(str, r0 ' + r4 ', st), fits(r4, sks3, st[r0 -- i ', refval(r4)]), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, fits(r0, sks, st), is_referencevalue(st[r0 -- i ', refval(r4)][r -- i ']), fits((st[r0 -- i ', refval(r4)][r -- i ']) .refval, sks1, st[r0 -- i ', refval(r4)]), is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ r1 = jvmref, r0 = r4, r0 = jvmref, sks + i ' ' + sks1 = i ' ' + sks3, sks3 = [], r4 = jvmref, r = jvmref, hasSharing(r0, st), hasSharing(r4, st), junkref(str, r0, st), is_classtype(st[r -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- sks2] .refval ≠ r0), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r0 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 227:
(st[r0 -- i ', refval(r4)][r -- i ']) = refval(r2), (st[r0 -- i ', refval(r4)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r4)][r0 -- sks]) = refval(r), validref(str, r4, ty, st), disjoint(str, r0 ' + r4 ', st), fits(r4, sks3, st[r0 -- i ', refval(r4)]), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, fits(r0, sks, st), is_referencevalue(st[r0 -- i ', refval(r4)][r -- i ']), fits(r2, sks1, st[r0 -- i ', refval(r4)]), is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ r1 = jvmref, r0 = r4, r0 = jvmref, sks + i ' ' + sks1 = i ' ' + sks3, sks3 = [], r4 = jvmref, r = jvmref, hasSharing(r0, st), hasSharing(r4, st), junkref(str, r0, st), is_classtype(st[r -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- sks2] .refval ≠ r0), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r0 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0)

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[r0 -- i ', refval(r4)][r -- i '], r2] 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[r0 -- i ', refval(r4)][r -- i '], r2)]]