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Proof step 11 from proof validrefs-putshort-field (previous step)

st[r0 -- i '] = refval(refs1 .first), 0 ≤ i, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), validrefs(str, refs1, st[r0 -- _type] .type .type, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), i < st[r0 -- _length] .intval, 0 < st[r0 -- _length] .intval, ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs1, ty, st), junkref(str, r0, st), is_array(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , fs ' ≠ _length ∧ fs ' ≠ _type → (is_array(str, r, st[r0 -- fs ', val]) ↔ is_array(str, r, st)) ,[val, fs, r0, st, r, str] → [shortval(sho), mkfs(class, short_type, fieldvar), r, st, r0, str] ,F ,okfuns , ,is_array-put-field ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ _length ≠ mkfs(class, short_type, fieldvar) '], [CSIMPSEQ : ⊦ mkfs (class1, short_type, fieldvar) ' ≠ _type])], [EXTRATERMS : (shortval(sho), mkfs(class, short_type, fieldvar), r, st, r0, str)]]