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Proof step 13 from proof pathex-put-cyclic (previous step)

st[r -- _type] .type = mkclasstype(class0), mkfs(class, mkclasstype(class1), fieldvar) ' ∈ instfields(class0), is_valid_ref(str, r, st), class0 ≤ class1 ⊦ r = jvmref, validrefs(str, r ' + r ', mkclasstype(class0), st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 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 7:
¬ ( is_obj(str, r, st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)]) ∧ (st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)][r -- _type]) .type ≤ mkclasstype(class0)), st[r -- _type] .type = mkclasstype(class0), mkfs(class, mkclasstype(class1), fieldvar) ' ∈ instfields(class0), is_valid_ref(str, r, st), class0 ≤ class1 ⊦ r = jvmref, validrefs(str, r ' + r ', mkclasstype(class0), st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)])
Proof step 12:
is_obj(str, r, st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)]) ∧ (st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)][r -- _type]) .type ≤ mkclasstype(class0), st[r -- _type] .type = mkclasstype(class0), mkfs(class, mkclasstype(class1), fieldvar) ' ∈ instfields(class0), is_valid_ref(str, r, st), class0 ≤ class1 ⊦ r = jvmref, r ' = [] ∨ (∃ fs. fs ' ∈ instfields((st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)][r -- _type]) .type .class) ∧ is_referencevalue(st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)][r -- fs ']) ∧ r ' .first = (st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)][r -- fs ']) .refval ∧ validrefs(str, r ', fs .type, st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)]))

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)], mkclasstype(class0), r ', r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- mkfs(class, mkclasstype(class1), fieldvar) ', refval(r)], mkclasstype(class0), r ', r, str)]]