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Proof step 213 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 211:
⊦ hasSharing(r, st) ↔ (∃ sks1, sks2. fits(r, sks1, st) ∧ fits(r, sks2, st) ∧ sks1 ≠ sks2 ∧ st[r -- sks1] .refval ≠ jvmref ∧ st[r -- sks1] = st[r -- sks2])
Proof step 212:
st[r2 -- sks3] = refval(r1), st[r -- _type] .type = mkarraytype(ty), st[r2 -- sks1] = refval(r1), is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]), 0 < st[r -- _length] .intval, fits(r2, sks1, st), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks3, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st) ⊦ r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks3 = [], sks1 = sks3, junkref(str, r, st), ∃ sks1, sks2. fits(r2, sks1, st) ∧ fits(r2, sks2, st) ∧ sks1 ≠ sks2 ∧ st[r2 -- sks1] .refval ≠ jvmref ∧ st[r2 -- sks1] = st[r2 -- sks2], hasSharing(r, st), ∃ sks, sks0. sks1 = sks + i ' ' + sks0 ∧ st[r2 -- sks] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ st[r2 -- sks] .refval), ∃ sks, sks0. sks3 = sks + i ' ' + sks0 ∧ st[r2 -- sks] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ st[r2 -- sks] .refval)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: hasSharing-def-better antecedent: succedent: hasSharing(r, st) ↔ (∃ sks1, sks2. fits(r, sks1, st) ∧ fits(r, sks2, st) ∧ sks1 ≠ sks2 ∧ st[r -- sks1] .refval ≠ jvmref ∧ st[r -- sks1] = st[r -- sks2]) substlist: [st, r] → [st, r2] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 7)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r2)]]