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Proof step 25 from proof validrefs-put-badarrayfield (previous step)

is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), validrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), is_obj(str, r, st[r0 -- fs ', val]) ∨ is_array(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) ⊦ fs ' = _type, fs ' = _length, r = jvmref, validrefs(str, r ' + acc, ty, st), junkref(str, r, st), dups((r ' + acc) .butlast)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ¬ is_arraytype(st[r -- _type] .type) → ¬ is_array(str, r, st)
Proof step 24:
¬ is_arraytype((st[r0 -- fs ', val][r -- _type]) .type), is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), validrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), is_obj(str, r, st[r0 -- fs ', val]) ∨ false, 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)

Rule argument

[speclemmaarg: ,¬ is_arraytype(st[r -- _type] .type) → ¬ is_array(str, r, st) ,[st, r, str] → [st[r0 -- fs ', val], r, str] ,F ,okfuns , ,is_array-arraytype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ is_arraytype (st[r -- _type] .type) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (st[r0 -- fs ', val], r, str)]]