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Proof step 28 from proof pathex-put-cyclic (previous step)

st[r0 -- _type] .type = mkclasstype(class0), validrefs(str, (r ' + refs0) + r0 ', st[r -- _type] .type, st), st[r -- _type] .type ≤ ty, mkfs(class, ty, fieldvar) ' ∈ instfields(class0), validrefs(str, r0 ', mkclasstype(class0), st) ⊦ _type = mkfs(class, ty, fieldvar) ', r = r0, r0 = jvmref, r = jvmref, validrefs(str, r0 ' + (r ' + refs0) + r0 ', mkclasstype(class0), st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), r ∈ refs0, dups(refs0), r0 ∈ refs0, is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[refs .first -- _type] .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 27:
st[r0 -- _type] .type = mkclasstype(class0), validrefs(str, (r ' + refs0) + r0 ', st[r -- _type] .type, st), st[r -- _type] .type ≤ ty, mkfs(class, ty, fieldvar) ' ∈ instfields(class0), r0 = jvmref ∨ r0 ≠ jvmref ∧ is_valid_ref(str, r0, st) ∧ st[r0 -- _type] .type ≤ mkclasstype(class0) ⊦ _type = mkfs(class, ty, fieldvar) ', r = r0, r0 = jvmref, r = jvmref, validrefs(str, r0 ' + (r ' + refs0) + r0 ', mkclasstype(class0), st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), r ∈ refs0, dups(refs0), r0 ∈ refs0, is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[refs .first -- _type] .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Rule argument

[crewrite-arg: validrefs-one , F , [st, ty, r, str] → [st, mkclasstype(class0), r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mkclasstype(class0), r0, str)]]