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Proof step 517 from proof hasSharing-put-index-refval (previous step)

st[r -- sks0] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- (sks + i ' ' + sks4)]) = refval(r1), st[r -- sks1] = refval(r0), st[r4 -- sks] = refval(r0), (st[r0 -- i ', refval(r4)][r4 -- sks]) = refval(r2), 0 < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks + i ' ' + sks4)]), fits(r, sks0, st), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks, st[r0 -- i ', refval(r4)]), fits(r2, i ' ' + sks4, st[r0 -- i ', refval(r4)]), i < st[r0 -- _length] .intval, 0 ≤ i ⊦ r4 = jvmref, sks1 = [], sks0 = sks1 + i ' ' + sks + i ' ' + sks4, sks0 = [], r1 = jvmref, r = r4, r0 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .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), ∃ sks1, sks2. sks0 = sks1 + i ' ' + sks2 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ st[r -- sks1] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ r0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 486:
⊦ ¬ (∃ 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 490:
¬ ( ¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r4 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r4 -- sks2] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length), st[r -- sks0] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- (sks + i ' ' + sks4)]) = refval(r1), st[r -- sks1] = refval(r0), st[r4 -- sks] = refval(r0), (st[r0 -- i ', refval(r4)][r4 -- sks]) = refval(r2), 0 < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks + i ' ' + sks4)]), fits(r, sks0, st), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks, st[r0 -- i ', refval(r4)]), fits(r2, i ' ' + sks4, st[r0 -- i ', refval(r4)]), i < st[r0 -- _length] .intval, 0 ≤ i ⊦ r4 = jvmref, sks1 = [], sks0 = sks1 + i ' ' + sks + i ' ' + sks4, sks0 = [], r1 = jvmref, r = r4, r0 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .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), ∃ sks1, sks2. sks0 = sks1 + i ' ' + sks2 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ st[r -- sks1] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ r0)
Proof step 516:
¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r4 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r4 -- sks2] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length, st[r -- sks0] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- (sks + i ' ' + sks4)]) = refval(r1), st[r -- sks1] = refval(r0), st[r4 -- sks] = refval(r0), (st[r0 -- i ', refval(r4)][r4 -- sks]) = refval(r2), 0 < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks + i ' ' + sks4)]), fits(r, sks0, st), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks, st), fits(r2, i ' ' + sks4, st[r0 -- i ', refval(r4)]), i < st[r0 -- _length] .intval, 0 ≤ i ⊦ r4 = jvmref, sks1 = [], sks0 = sks1 + i ' ' + sks + i ' ' + sks4, sks0 = [], r1 = jvmref, r = r4, r0 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .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), ∃ sks1, sks2. sks0 = sks1 + i ' ' + sks2 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ st[r -- sks1] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .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(r4), i ', r0, st, sks, r4] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 12)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refval(r4), i ', r0, st, sks, r4)]]