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Proof step 13 from proof validrefs-putshort-field (previous step)

st[r0 -- i '] = refval(refs1 .first), 0 < (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- _length]) .intval, 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[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][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

Proof step 9:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 12:
r0 -- _length ≠ r -- mkfs(class, short_type, fieldvar) ', st[r0 -- i '] = refval(refs1 .first), 0 < st[r0 -- _length] .intval, 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, ∀ 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)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r0 -- _length, shortval(sho), r -- mkfs(class, short_type, fieldvar) ', st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ _length ≠ mkfs(class, short_type, fieldvar) '])], [EXTRATERMS : (r0 -- _length, shortval(sho), r -- mkfs(class, short_type, fieldvar) ', st)]]