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Proof step 21 from proof validrefs-put-badarrayfield (previous step)

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, validrefs(str, r ' + acc, ty, st), junkref(str, r, st), dups((r ' + acc) .butlast), is_arraytype(st[r -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 20:
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)

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, ty, acc, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc, r, str)]]