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Proof step 373 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 356:
⊦ ¬ (∃ 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 360:
¬ ¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r3 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r3 -- sks2] .refval ≠ r0)), (st[r0 -- i ', refval(r3)][r3 -- sks]) = refval(r2), st[r3 -- sks] = refval(r0), (st[r0 -- i ', refval(r3)][r3 -- (sks + i ' ' + sks0)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r3)][r3 -- sks3]) = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r3)][r2 -- i ']) = refval(r4), fits(r4, sks0, st[r0 -- i ', refval(r3)]), fits(r3, sks, st), is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks + i ' ' + sks0)]), 0 < st[r0 -- _length] .intval, validref(str, r3, ty, st), disjoint(str, r ' + r3 ', st), fits(r, sks1, st), fits(r3, sks3, st[r0 -- i ', refval(r3)]), i < st[r0 -- _length] .intval, 0 ≤ i, is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks3)]), is_arraytype(st[r2 -- _type] .type) → i < st[r2 -- _length] .intval ⊦ r2 = jvmref, sks + i ' ' + sks0 = sks3, r1 = jvmref, r = r3, r0 = jvmref, sks1 = [], r3 = jvmref, is_classtype(st[r2 -- _type] .type), hasSharing(r, st), hasSharing(r3, st), junkref(str, r, st), ∃ sks4, sks5. sks = sks4 + i ' ' + sks5 ∧ st[r3 -- sks4] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks4 → st[r3 -- sks2] .refval ≠ st[r3 -- sks4] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r3 -- sks4] .refval ≠ r0), ∃ 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 ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ r0), ∃ sks0, sks4. sks1 = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval)
Proof step 372:
¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r3 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r3 -- sks2] .refval ≠ r0)), st[r3 -- sks] = refval(r2), st[r3 -- sks] = refval(r0), (st[r0 -- i ', refval(r3)][r3 -- (sks + i ' ' + sks0)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r3)][r3 -- sks3]) = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r3)][r2 -- i ']) = refval(r4), fits(r4, sks0, st[r0 -- i ', refval(r3)]), fits(r3, sks, st), is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks + i ' ' + sks0)]), 0 < st[r0 -- _length] .intval, validref(str, r3, ty, st), disjoint(str, r ' + r3 ', st), fits(r, sks1, st), fits(r3, sks3, st[r0 -- i ', refval(r3)]), i < st[r0 -- _length] .intval, 0 ≤ i, is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks3)]), is_arraytype(st[r2 -- _type] .type) → i < st[r2 -- _length] .intval ⊦ r2 = jvmref, sks + i ' ' + sks0 = sks3, r1 = jvmref, r = r3, r0 = jvmref, sks1 = [], r3 = jvmref, is_classtype(st[r2 -- _type] .type), hasSharing(r, st), hasSharing(r3, st), junkref(str, r, st), ∃ sks4, sks5. sks = sks4 + i ' ' + sks5 ∧ st[r3 -- sks4] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks4 → st[r3 -- sks2] .refval ≠ st[r3 -- sks4] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r3 -- sks4] .refval ≠ r0), ∃ 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 ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ r0), ∃ sks0, sks4. sks1 = 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: 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, r3, refval(r3), 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, r3, refval(r3), i ', r0, st)]]