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Proof step 70 from proof hasSharing-put-index-refval (previous step)

st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r2 -- sks1]) = refval(r2), 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, 0 ≤ i, disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r2, sks1, st[r -- i ', refval(r2)]) ⊦ r = jvmref, r = r2, r2 = jvmref, sks1 = [], junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ ¬ (∃ 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 56:
¬ ( ¬ (∃ sks0, sks2. sks1 = sks0 + (i ' + sks2) ∧ st[r2 -- sks0] .refval = r ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r2 -- sks2] .refval ≠ r)) ∧ i ' ≠ _type ∧ i ' ≠ _length), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r2 -- sks1]) = refval(r2), 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, 0 ≤ i, disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r2, sks1, st[r -- i ', refval(r2)]) ⊦ r = jvmref, r = r2, r2 = jvmref, sks1 = [], junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st)
Proof step 69:
¬ (∃ sks0, sks2. sks1 = sks0 + (i ' + sks2) ∧ st[r2 -- sks0] .refval = r ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r2 -- sks2] .refval ≠ r)) ∧ i ' ≠ _type ∧ i ' ≠ _length, st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r2 -- sks1]) = refval(r2), 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, 0 ≤ i, disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r2, sks1, st) ⊦ r = jvmref, r = r2, r2 = jvmref, sks1 = [], junkref(str, r, st), hasSharing(r2, st), hasSharing(r, 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(r2), i ', r, st, sks1, r2] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 7)) dummy: () ]

Additional information

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