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Proof step 58 from proof junkrefs-put-notin-butlast (previous step)

is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- _type]) .type ≤ ty, acc + r ' = r1 ' + refs, st[r0 -- _type] .type ≤ ty, r ∈ st, okval(val, ty0), okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, is_array(str, r0, st), ∀ r, fs, st, val, str, ty. r -- fs ' ∈ st ∧ okval(st[r -- fs '], fs .type) ∧ okval(val, fs .type) ∧ r ∈ st → (junkrefs(str, acc + r ', ty, st[r -- fs ', val]) ↔ junkrefs(str, acc + r ', ty, st)) ∨ fs ' = _type ∨ fs ' = _length ∨ r ∈ acc ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r0 = jvmref, r = r0, acc + r ' ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- _length]) .intval ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- i ']) ∧ (acc + r ') .first = (st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- i ']) .refval ∧ junkrefs(str, acc + r ', (st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st)), r ∈ acc, r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
acc + r ' = r1 ' + refs, is_array(str, r0, st), r -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), okval(val, ty0), r ∈ st, st[r0 -- _type] .type ≤ ty, ∀ r, fs, st, val, str, ty. r -- fs ' ∈ st ∧ okval(st[r -- fs '], fs .type) ∧ okval(val, fs .type) ∧ r ∈ st → (junkrefs(str, acc + r ', ty, st[r -- fs ', val]) ↔ junkrefs(str, acc + r ', ty, st)) ∨ fs ' = _type ∨ fs ' = _length ∨ r ∈ acc ⊦ r = r0, r0 = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ junkrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st)), r ∈ acc, ¬ r1 ∈ acc ∧ r1 ≠ r, r ≠ r1 ∧ ¬ r ∈ refs

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ fs ' ≠ _length ∧ fs ' ≠ _type → ( is_array (str, r, st[r0 -- fs ', val]) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + r ' ≠ []])]]