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Proof step 46 from proof validrefs-put-badarrayfield (previous step)

is_array(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_array(str, r, st), is_arraytype(st[r0 -- _type] .type), acc = [] ∨ (∃ i. 0 ≤ i ∧ i < (st[r0 -- fs ', val][r -- _length]) .intval ∧ is_referencevalue(st[r0 -- fs ', val][r -- i ']) ∧ acc .first = (st[r0 -- fs ', val][r -- i ']) .refval ∧ validrefs(str, acc, (st[r0 -- fs ', val][r -- _type]) .type .type, st[r0 -- fs ', val])), st[r -- _type] .type ≤ ty, ∀ st, r0, str, ty, fs, val. is_arraytype(st[r0 -- _type] .type) ∧ validrefs(str, acc, ty, st[r0 -- fs ', val]) → fs ' = _type ∨ fs ' = _length ∨ acc = [] ∨ validrefs(str, acc, ty, st) ∨ junkref(str, acc .first, st) ∨ dups(acc .butlast) ⊦ fs ' = _type, fs ' = _length, r = jvmref, validrefs(str, r ' + acc, ty, st), junkref(str, r, st), dups((r ' + acc) .butlast), is_classtype(st[r -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
is_arraytype(st[r0 -- _type] .type), is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ st, r0, str, ty, fs, val. is_arraytype(st[r0 -- _type] .type) ∧ validrefs(str, acc, ty, st[r0 -- fs ', val]) → fs ' = _type ∨ fs ' = _length ∨ acc = [] ∨ validrefs(str, acc, ty, st) ∨ junkref(str, acc .first, st) ∨ dups(acc .butlast), acc = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(str, acc, st[r -- _type] .type .type, st[r0 -- fs ', val]) ⊦ fs ' = _type, fs ' = _length, r = jvmref, validrefs(str, r ' + acc, ty, st), junkref(str, r, st), dups((r ' + acc) .butlast), is_classtype(st[r -- _type] .type)

Rule argument

[emptyarg]

Additional information

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