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Proof step 23 from proof validrefs-not-contains (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ', ty0, st) ⊦ r0 = jvmref, r = r0, r = jvmref, contains(str, st[r -- _type] .type, st[r0 -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 22:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), r0 = jvmref ∨ r0 ≠ jvmref ∧ is_valid_ref(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty0 ⊦ r0 = jvmref, r = r0, r = jvmref, contains(str, st[r -- _type] .type, st[r0 -- _type] .type)

Rule argument

[speclemmaarg: , validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty ,[st, ty, r, str] → [st, ty0, r0, str] ,F ,cyclic , ,validrefs-one ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty0, r0, str)]]