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Proof step 461 from proof hasSharing-put-index-refval (previous step)

(st[r0 -- i ', refval(r4)][r -- (sks + i ' ' + sks2)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r -- sks1] = refval(r0), st[r -- sks] = refval(r0), (st[r0 -- i ', refval(r4)][r -- sks]) = refval(r2), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks3, st[r0 -- i ', refval(r4)]), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks3)]), fits(r, sks, st), is_referencevalue(st[r0 -- i ', refval(r4)][r2 -- i ']), fits((st[r0 -- i ', refval(r4)][r2 -- i ']) .refval, sks2, st[r0 -- i ', refval(r4)]), r4 = jvmref → is_reftype(ty), is_arraytype(st[r2 -- _type] .type) → i < st[r2 -- _length] .intval ⊦ sks1 = [], sks + i ' ' + sks2 = sks1 + i ' ' + sks3, r1 = jvmref, r = r4, r0 = jvmref, r2 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), is_classtype(st[r2 -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0), ∃ sks0, sks2. sks1 = sks0 + i ' ' + sks2 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ r0), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 460:
(st[r0 -- i ', refval(r4)][r2 -- i ']) = refval(r3), (st[r0 -- i ', refval(r4)][r -- (sks + i ' ' + sks2)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r -- sks1] = refval(r0), st[r -- sks] = refval(r0), (st[r0 -- i ', refval(r4)][r -- sks]) = refval(r2), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks3, st[r0 -- i ', refval(r4)]), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks3)]), fits(r, sks, st), is_referencevalue(st[r0 -- i ', refval(r4)][r2 -- i ']), fits(r3, sks2, st[r0 -- i ', refval(r4)]), r4 = jvmref → is_reftype(ty), is_arraytype(st[r2 -- _type] .type) → i < st[r2 -- _length] .intval ⊦ sks1 = [], sks + i ' ' + sks2 = sks1 + i ' ' + sks3, r1 = jvmref, r = r4, r0 = jvmref, r2 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), is_classtype(st[r2 -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0), ∃ sks0, sks2. sks1 = sks0 + i ' ' + sks2 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ r0), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .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[r0 -- i ', refval(r4)][r2 -- i '], r3] 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)][r2 -- i '], r3)]]