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Proof step 78 from proof hasSharing-put-index-refval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ ¬ (∃ 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 23:
¬ ( ¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r0 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length), (st[r0 -- i ', refval(r1)][r0 -- sks]) = refval(r), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r1)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r -- i ']) = refval(r2), fits(r2, sks1, st[r0 -- i ', refval(r1)]), fits(r0, sks, st[r0 -- i ', refval(r1)]), validref(str, r1, ty, st), disjoint(str, r0 ' + r1 ', st), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ r = jvmref, r1 = jvmref, r0 = r1, r0 = jvmref, sks + i ' ' + sks1 = i ' ', is_classtype(st[r -- _type] .type), hasSharing(r0, st), hasSharing(r1, st), junkref(str, r0, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- sks2] .refval ≠ r0)
Proof step 77:
¬ (∃ sks0, sks1. sks = sks0 + (i ' + sks1) ∧ st[r0 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length, (st[r0 -- i ', refval(r1)][r0 -- sks]) = refval(r), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r1)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r -- i ']) = refval(r2), fits(r2, sks1, st[r0 -- i ', refval(r1)]), fits(r0, sks, st), validref(str, r1, ty, st), disjoint(str, r0 ' + r1 ', st), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ r = jvmref, r1 = jvmref, r0 = r1, r0 = jvmref, sks + i ' ' + sks1 = i ' ', is_classtype(st[r -- _type] .type), hasSharing(r0, st), hasSharing(r1, st), junkref(str, r0, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- 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(r1), i ', r0, st, sks, r0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 6)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refval(r1), i ', r0, st, sks, r0)]]