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Proof step 783 from proof hasSharing-put-index-refval (previous step)

(st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r -- sks1]) = refval(r3), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st[r0 -- i ', refval(r2)]), fits(r3, i ' ' + sks2, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ sks1 + i ' ' + sks2 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 585:
⊦ ¬ (∃ sks0, sks1. sks = sks0 + (sk + sks1) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + sk ⊑ sks0 → st[r -- sks2] .refval ≠ r0)) ∧ sk ≠ _type ∧ sk ≠ _length → (fits(r, sks, st[r0 -- sk, val]) ↔ fits(r, sks, st))
Proof step 589:
¬ ( ¬ (∃ sks0, sks2. sks1 = sks0 + (i ' + sks2) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r -- sks2] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r -- sks1]) = refval(r3), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st[r0 -- i ', refval(r2)]), fits(r3, i ' ' + sks2, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ sks1 + i ' ' + sks2 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0)
Proof step 782:
¬ (∃ sks0, sks2. sks1 = sks0 + (i ' + sks2) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r -- sks2] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length, (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r -- sks1]) = refval(r3), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r3, i ' ' + sks2, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ sks1 + i ' ' + sks2 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-put-other antecedent: succedent: ¬ (∃ sks0, sks1. sks = sks0 + (sk + sks1) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + sk ⊑ sks0 → st[r -- sks2] .refval ≠ r0)) ∧ sk ≠ _type ∧ sk ≠ _length → (fits(r, sks, st[r0 -- sk, val]) ↔ fits(r, sks, st)) substlist: [val, sk, r0, st, sks, r] → [refval(r2), i ', r0, st, sks1, r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 8)) dummy: () ]

Additional information

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