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Proof step 171 from proof addarray-disjoint-nosharing-01 (previous step)

(addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), (addarray(r, ty, vals, st)[r -- sks]) = refval(r0), newref(r, st), validreflist(str, vals, ty, st), disjoint(str, vals .nonnullrefs, st), fits(r, sks, addarray(r, ty, vals, st)), fits(r, sks0, addarray(r, ty, vals, st)) ⊦ sks0 = sks, sks0 = [], sks = [], r0 = jvmref, r = jvmref, hasSharing(vals .nonnullrefs, st), dups(vals .nonnullrefs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 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 170:
sks ≠ [], (addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), (addarray(r, ty, vals, st)[r -- sks]) = refval(r0), newref(r, st), validreflist(str, vals, ty, st), disjoint(str, vals .nonnullrefs, st), r ≠ jvmref ∧ is_referencevalue(addarray(r, ty, vals, st)[r -- sks .first]) ∧ (is_classtype((addarray(r, ty, vals, st)[r -- _type]) .type) → sks .first ∈ instfields((addarray(r, ty, vals, st)[r -- _type]) .type .class)) ∧ ( is_arraytype((addarray(r, ty, vals, st)[r -- _type]) .type) → is_indexkey(sks .first) ∧ 0 ≤ sks .first .index ∧ sks .first .index < (addarray(r, ty, vals, st)[r -- _length]) .intval) ∧ fits((addarray(r, ty, vals, st)[r -- sks .first]) .refval, sks .rest, addarray(r, ty, vals, st)), fits(r, sks0, addarray(r, ty, vals, st)) ⊦ sks0 = sks, sks0 = [], sks = [], r0 = jvmref, r = jvmref, 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), sks, 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), sks, r)]]