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Proof step 16 from proof validrefs-put-last (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r1 ', ty0, st[r1 -- sk, val]) ⊦ sk = _type, r1 = r, r = jvmref, junkref(str, r, st), validrefs(str, r1 ', ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 15:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), r1 = jvmref ∨ r1 ≠ jvmref ∧ is_valid_ref(str, r1, st[r1 -- sk, val]) ∧ (st[r1 -- sk, val][r1 -- _type]) .type ≤ ty0 ⊦ sk = _type, r1 = r, r = jvmref, junkref(str, r, st), validrefs(str, r1 ', ty0, st)

Rule argument

[crewrite-arg: validrefs-one , F , [st, ty, r, str] → [st[r1 -- sk, val], ty0, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r1 -- sk, val], ty0, r1, str)]]