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Proof step 459 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 332:
⊦ ¬ (∃ sks0, sks1. sks = sks0 + (sk + sks1) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + sk ⊑ sks0 → st[r -- sks2] .refval ≠ r0)) → (st[r0 -- sk, val][r -- sks]) = st[r -- sks]
Proof step 336:
¬ ¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r -- sks2] .refval ≠ r0)), (st[r0 -- i ', refval(r4)][r -- sks]) = refval(r2), st[r -- sks] = refval(r0), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r -- (sks + i ' ' + sks2)]) = refval(r1), (st[r0 -- i ', refval(r4)][r2 -- i ']) = refval(r3), fits(r3, sks2, st[r0 -- i ', refval(r4)]), fits(r, sks, st), is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks3)]), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, fits(r4, sks3, st[r0 -- i ', refval(r4)]), fits(r, sks1, st), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), is_arraytype(st[r2 -- _type] .type) → i < st[r2 -- _length] .intval, r4 = jvmref → is_reftype(ty) ⊦ r2 = jvmref, r0 = jvmref, r = r4, r1 = jvmref, sks + i ' ' + sks2 = sks1 + i ' ' + sks3, sks1 = [], is_classtype(st[r2 -- _type] .type), junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r -- sks4] .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), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0)
Proof step 458:
¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r -- sks2] .refval ≠ r0)), st[r -- sks] = refval(r2), st[r -- sks] = refval(r0), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r -- (sks + i ' ' + sks2)]) = refval(r1), (st[r0 -- i ', refval(r4)][r2 -- i ']) = refval(r3), fits(r3, sks2, st[r0 -- i ', refval(r4)]), fits(r, sks, st), is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks3)]), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, fits(r4, sks3, st[r0 -- i ', refval(r4)]), fits(r, sks1, st), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), is_arraytype(st[r2 -- _type] .type) → i < st[r2 -- _length] .intval, r4 = jvmref → is_reftype(ty) ⊦ r2 = jvmref, r0 = jvmref, r = r4, r1 = jvmref, sks + i ' ' + sks2 = sks1 + i ' ' + sks3, sks1 = [], is_classtype(st[r2 -- _type] .type), junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r -- sks4] .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), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0)

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-put-other antecedent: succedent: ¬ (∃ sks0, sks1. sks = sks0 + (sk + sks1) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + sk ⊑ sks0 → st[r -- sks2] .refval ≠ r0)) → (st[r0 -- sk, val][r -- sks]) = st[r -- sks] substlist: [sks, r, val, sk, r0, st] → [sks, r, refval(r4), i ', r0, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks, r, refval(r4), i ', r0, st)]]