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Proof step 777 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 596:
⊦ sks ≠ [] ∧ sks0 ≠ [] → st[r -- (sks + sks0)] = st[st[r -- sks] .refval -- sks0]
Proof step 686:
¬ (sks1 ≠ [] ∧ i ' ' + sks2 ≠ []), st[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r -- sks1] = refval(r0), fits(r2, sks2, st[r0 -- i ', refval(r2)]), fits(r, sks1, st), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks2 = sks, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks0, sks3. sks1 = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval)
Proof step 776:
sks1 ≠ [] ∧ i ' ' + sks2 ≠ [], st[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][(st[r0 -- i ', refval(r2)][r -- sks1]) .refval -- (i ' ' + sks2)]) = refval(r1), st[r -- sks1] = refval(r0), fits(r2, sks2, st[r0 -- i ', refval(r2)]), fits(r, sks1, st), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks2 = sks, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks0, sks3. sks1 = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval)

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-append antecedent: succedent: sks ≠ [] ∧ sks0 ≠ [] → st[r -- (sks + sks0)] = st[st[r -- sks] .refval -- sks0] substlist: [sks0, sks, r, st] → [i ' ' + sks2, sks1, r, st[r0 -- i ', refval(r2)]] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i ' ' + sks2, sks1, r, st[r0 -- i ', refval(r2)])]]