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Proof step 272 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 258:
⊦ ¬ (∃ 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 262:
¬ ¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r4 -- sks0] .refval = r ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r4 -- sks2] .refval ≠ r)), (st[r -- i ', refval(r4)][r4 -- sks]) = refval(r0), st[r4 -- sks] = refval(r), (st[r -- i ', refval(r4)][r4 -- (sks + i ' ' + sks1)]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), st[r -- sks0] = refval(r1), (st[r -- i ', refval(r4)][r0 -- i ']) = refval(r2), fits(r2, sks1, st[r -- i ', refval(r4)]), fits(r4, sks, st), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), fits(r, sks0, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval ⊦ r0 = jvmref, r4 = jvmref, sks0 = i ' ' + sks + i ' ' + sks1, r = jvmref, r = r4, r1 = jvmref, sks0 = [], is_classtype(st[r0 -- _type] .type), junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), ∃ sks3, sks4. sks = sks3 + i ' ' + sks4 ∧ st[r4 -- sks3] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks3 → st[r4 -- sks2] .refval ≠ st[r4 -- sks3] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ r), ∃ sks2, sks1. sks0 = sks2 + i ' ' + sks1 ∧ st[r -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r -- sks3] .refval ≠ r)
Proof step 271:
¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r4 -- sks0] .refval = r ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r4 -- sks2] .refval ≠ r)), st[r4 -- sks] = refval(r0), st[r4 -- sks] = refval(r), (st[r -- i ', refval(r4)][r4 -- (sks + i ' ' + sks1)]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), st[r -- sks0] = refval(r1), (st[r -- i ', refval(r4)][r0 -- i ']) = refval(r2), fits(r2, sks1, st[r -- i ', refval(r4)]), fits(r4, sks, st), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), fits(r, sks0, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval ⊦ r0 = jvmref, r4 = jvmref, sks0 = i ' ' + sks + i ' ' + sks1, r = jvmref, r = r4, r1 = jvmref, sks0 = [], is_classtype(st[r0 -- _type] .type), junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), ∃ sks3, sks4. sks = sks3 + i ' ' + sks4 ∧ st[r4 -- sks3] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks3 → st[r4 -- sks2] .refval ≠ st[r4 -- sks3] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ r), ∃ sks2, sks1. sks0 = sks2 + i ' ' + sks1 ∧ st[r -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r -- sks3] .refval ≠ r)

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, r4, refval(r4), i ', r, 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, r4, refval(r4), i ', r, st)]]