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Proof step 740 from proof hasSharing-put-index-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r2 -- sks0] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- sks0]) = refval(r3), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r2, sks0, st[r0 -- i ', refval(r2)]), fits(r3, i ' ' + sks3, st[r0 -- i ', refval(r2)]) ⊦ sks1 = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, r2 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r2 -- sks4] .refval ≠ r0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 711:
⊦ ¬ (∃ 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 715:
¬ ( ¬ (∃ sks2, sks1. sks0 = sks2 + (i ' + sks1) ∧ st[r2 -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + i ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r2 -- sks0] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- sks0]) = refval(r3), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r2, sks0, st[r0 -- i ', refval(r2)]), fits(r3, i ' ' + sks3, st[r0 -- i ', refval(r2)]) ⊦ sks1 = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, r2 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r2 -- sks4] .refval ≠ r0)
Proof step 739:
¬ (∃ sks2, sks1. sks0 = sks2 + (i ' + sks1) ∧ st[r2 -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + i ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length, st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r2 -- sks0] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- sks0]) = refval(r3), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r2, sks0, st), fits(r3, i ' ' + sks3, st[r0 -- i ', refval(r2)]) ⊦ sks1 = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, r2 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r2 -- sks4] .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, sks0, r2] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 13)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refval(r2), i ', r0, st, sks0, r2)]]