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Proof step 33 from proof validrefs-putshort-field (previous step)

st[r0 -- i '] = refval(refs1 .first), is_array(str, r0, st), 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, refs1 = [], junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ refs1 .first = st[r0 -- i0 '] .refval ∧ validrefs(str, refs1, st[r0 -- _type] .type .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
refs1 = r1 + refs0, st[r0 -- i '] = refval(r1), is_array(str, r0, st), 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, refs1 = [], junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r1 = st[r0 -- i0 '] .refval ∧ validrefs(str, refs1, st[r0 -- _type] .type .type, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs1, r1, refs0] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs1, r1, refs0)]]