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Proof step 56 from proof validrefs-put-badarrayfield (previous step)

is_arraytype(st[r0 -- _type] .type), validrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), ∀ 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, 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 1:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 55:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st[r0 -- fs ', val]) ∨ ¬ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty)), is_arraytype(st[r0 -- _type] .type), validrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), ∀ 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, validrefs(str, r ' + acc, ty, st), junkref(str, r, st), dups((r ' + acc) .butlast)

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st[r0 -- fs ', val], ty, acc, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- fs ', val], ty, acc, r, str)]]