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Proof step 110 from proof hasSharing-put-index-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r0 -- sks0]) = refval(r1), disjoint(str, r0 ' + r1 ', st), validref(str, r1, ty, st), fits(r0, sks0, st[r0 -- i ', refval(r1)]), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval ⊦ sks0 = i ' ', r0 = jvmref, r0 = r1, r1 = jvmref, sks0 = [], junkref(str, r0, st), hasSharing(r1, st), hasSharing(r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ ¬ (∃ 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 89:
¬ ( ¬ (∃ sks2, sks1. sks0 = sks2 + (i ' + sks1) ∧ st[r0 -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + i ' ⊑ sks2 → st[r0 -- sks3] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r0 -- sks0]) = refval(r1), disjoint(str, r0 ' + r1 ', st), validref(str, r1, ty, st), fits(r0, sks0, st[r0 -- i ', refval(r1)]), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval ⊦ sks0 = i ' ', r0 = jvmref, r0 = r1, r1 = jvmref, sks0 = [], junkref(str, r0, st), hasSharing(r1, st), hasSharing(r0, st)
Proof step 109:
¬ (∃ sks2, sks1. sks0 = sks2 + (i ' + sks1) ∧ st[r0 -- sks2] .refval = r0 ∧ (∀ sks3. sks3 + i ' ⊑ sks2 → st[r0 -- sks3] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length, st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r0 -- sks0]) = refval(r1), disjoint(str, r0 ' + r1 ', st), validref(str, r1, ty, st), fits(r0, sks0, st), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval ⊦ sks0 = i ' ', r0 = jvmref, r0 = r1, r1 = jvmref, sks0 = [], junkref(str, r0, st), hasSharing(r1, st), hasSharing(r0, st)

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, sks0, r0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 4)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refval(r1), i ', r0, st, sks0, r0)]]