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Proof step 20 from proof validrefs-put-badarrayfield (previous step)

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), is_obj(str, r, 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), acc = [] ∨ fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ', val][r -- fs0 ']) ∧ acc .first = (st[r0 -- fs ', val][r -- fs0 ']) .refval ∧ validrefs(str, acc, fs0 .type, st[r0 -- fs ', val]) ⊦ fs ' = _type, fs ' = _length, r = jvmref, acc = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)), junkref(str, r, st), dups((r ' + acc) .butlast), is_arraytype(st[r -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
acc .first = (st[r0 -- fs ', val][r -- fs0 ']) .refval, is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, fs0 ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r0 -- fs ', val][r -- fs0 ']), validrefs(str, acc, fs0 .type, st[r0 -- fs ', val]), ∀ st0, r1, str0, ty0, fs1, val0. is_arraytype(st0[r1 -- _type] .type) ∧ validrefs(str0, acc, ty0, st0[r1 -- fs1 ', val0]) → fs1 ' = _type ∨ fs1 ' = _length ∨ validrefs(str0, acc, ty0, st0) ∨ junkref(str0, acc .first, st0) ⊦ fs ' = _type, fs ' = _length, r = jvmref, acc = [], is_arraytype(st[r -- _type] .type), junkref(str, r, st), dups(acc .butlast), r ∈ acc .butlast, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs ≠ [] → (refs0 + refs) .butlast = refs0 + refs .butlast])]]