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Proof step 658 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 619:
⊦ ¬ (∃ 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 623:
¬ ¬ (∃ sks2, sks1. sks0 = sks2 + (i ' + sks1) ∧ st[r2 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ r)), st[r -- sks] = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][(st[r -- i ', refval(r2)][r2 -- sks0]) .refval -- (i ' ' + sks1)]) = refval(r1), st[r2 -- sks0] = refval(r), 0 < st[r -- _length] .intval, fits(r2, sks0 + i ' ' + sks1, st[r -- i ', refval(r2)]), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r -- _length] .intval, 0 ≤ i ⊦ i ' ' + sks0 + i ' ' + sks1 = sks, r = jvmref, r = r2, r1 = jvmref, sks = [], r2 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks0 → st[r2 -- sks3] .refval ≠ r)
Proof step 657:
¬ (∃ sks2, sks1. sks0 = sks2 + (i ' + sks1) ∧ st[r2 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ r)), st[r -- sks] = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][st[r2 -- sks0] .refval -- (i ' ' + sks1)]) = refval(r1), st[r2 -- sks0] = refval(r), 0 < st[r -- _length] .intval, fits(r2, sks0 + i ' ' + sks1, st[r -- i ', refval(r2)]), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r -- _length] .intval, 0 ≤ i ⊦ i ' ' + sks0 + i ' ' + sks1 = sks, r = jvmref, r = r2, r1 = jvmref, sks = [], r2 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks0 → st[r2 -- 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] → [sks0, r2, refval(r2), i ', r, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks0, r2, refval(r2), i ', r, st)]]