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Proof step 383 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 348:
⊦ fits(r, sks + sks0, st) ↔ fits(r, sks, st) ∧ fits(st[r -- sks] .refval, sks0, st)
Proof step 382:
st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r3)][r3 -- sks3]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r3)][r3 -- (sks + i ' ' + sks0)]) = refval(r1), st[r3 -- sks] = refval(r0), 0 < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks + i ' ' + sks0)]), fits(r3, sks, st[r0 -- i ', refval(r3)]) ∧ fits((st[r0 -- i ', refval(r3)][r3 -- sks]) .refval, i ' ' + sks0, st[r0 -- i ', refval(r3)]), is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks3)]), 0 ≤ i, i < st[r0 -- _length] .intval, fits(r3, sks3, st[r0 -- i ', refval(r3)]), fits(r, sks1, st), disjoint(str, r ' + r3 ', st), validref(str, r3, ty, st) ⊦ r3 = jvmref, sks1 = [], r0 = jvmref, r = r3, r1 = jvmref, sks + i ' ' + sks0 = sks3, junkref(str, r, st), hasSharing(r3, st), hasSharing(r, st), ∃ sks0, sks4. sks1 = sks0 + i ' ' + sks4 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r -- sks5] .refval ≠ st[r -- sks0] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks1 → 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), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks → st[r3 -- sks4] .refval ≠ r0)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-append antecedent: succedent: fits(r, sks + sks0, st) ↔ fits(r, sks, st) ∧ fits(st[r -- sks] .refval, sks0, st) substlist: [st, sks0, sks, r] → [st[r0 -- i ', refval(r3)], i ' ' + sks0, sks, r3] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 7)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- i ', refval(r3)], i ' ' + sks0, sks, r3)]]