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Proof step 163 from proof addarray-disjoint-nosharing-01 (previous step)

(addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]) = refval(r0), (addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), vals[i→n(i)] = refval(r1), 0 ≤ i, fits(r1, sks1, addarray(r, ty, vals, st)), fits(r, sks0, addarray(r, ty, vals, st)), i < n→i(# vals), newref(r, st), validreflist(str, vals, ty, st), disjoint(str, vals .nonnullrefs, st) ⊦ sks0 = i ' ' + sks1, sks0 = [], r0 = jvmref, r = jvmref, vals = [], hasSharing(vals .nonnullrefs, st), dups(vals .nonnullrefs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ sks ≠ [] → ( fits(r, sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sks .first]) ∧ (is_classtype(st[r -- _type] .type) → sks .first ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sks .first) ∧ 0 ≤ sks .first .index ∧ sks .first .index < st[r -- _length] .intval) ∧ fits(st[r -- sks .first] .refval, sks .rest, st))
Proof step 162:
sks0 ≠ [], (addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]) = refval(r0), (addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), vals[i→n(i)] = refval(r1), 0 ≤ i, fits(r1, sks1, addarray(r, ty, vals, st)), r ≠ jvmref ∧ is_referencevalue(addarray(r, ty, vals, st)[r -- sks0 .first]) ∧ (is_classtype((addarray(r, ty, vals, st)[r -- _type]) .type) → sks0 .first ∈ instfields((addarray(r, ty, vals, st)[r -- _type]) .type .class)) ∧ ( is_arraytype((addarray(r, ty, vals, st)[r -- _type]) .type) → is_indexkey(sks0 .first) ∧ 0 ≤ sks0 .first .index ∧ sks0 .first .index < (addarray(r, ty, vals, st)[r -- _length]) .intval) ∧ fits((addarray(r, ty, vals, st)[r -- sks0 .first]) .refval, sks0 .rest, addarray(r, ty, vals, st)), i < n→i(# vals), newref(r, st), validreflist(str, vals, ty, st), disjoint(str, vals .nonnullrefs, st) ⊦ sks0 = i ' ' + sks1, sks0 = [], r0 = jvmref, r = jvmref, vals = [], hasSharing(vals .nonnullrefs, st), dups(vals .nonnullrefs)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-rec antecedent: succedent: sks ≠ [] → ( fits(r, sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sks .first]) ∧ ( is_classtype(st[r -- _type] .type) → sks .first ∈ instfields(st[r -- _type] .type .class)) ∧ ( is_arraytype(st[r -- _type] .type) → is_indexkey(sks .first) ∧ 0 ≤ sks .first .index ∧ sks .first .index < st[r -- _length] .intval) ∧ fits(st[r -- sks .first] .refval, sks .rest, st)) substlist: [st, sks, r] → [addarray(r, ty, vals, st), sks0, r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 5)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, ty, vals, st), sks0, r)]]