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Proof step 50 from proof pathex-put-cyclic (previous step)

st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st) ⊦ r = jvmref, r0 = jvmref, r = r0, _type = mkfs(class, ty, fieldvar) ', r0 ∈ refs0, dups(refs0), r ∈ refs0, validrefs(str, r0 ' + r ' + refs0 + r0 ', mkclasstype(class0), 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 19:
⊦ 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 33:
¬ ( is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]) ∧ (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- _type]) .type ≤ mkclasstype(class0)), st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st) ⊦ r = jvmref, r0 = jvmref, r = r0, _type = mkfs(class, ty, fieldvar) ', r0 ∈ refs0, dups(refs0), r ∈ refs0, validrefs(str, r0 ' + r ' + refs0 + r0 ', mkclasstype(class0), 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)])
Proof step 49:
is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]) ∧ (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- _type]) .type ≤ mkclasstype(class0), st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st) ⊦ r = jvmref, r0 = jvmref, r = r0, _type = mkfs(class, ty, fieldvar) ', r0 ∈ refs0, dups(refs0), r ∈ refs0, r ' + refs0 + r0 ' = [] ∨ (∃ fs. fs ' ∈ instfields((st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- _type]) .type .class) ∧ is_referencevalue(st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- fs ']) ∧ (r ' + refs0 + r0 ') .first = (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- fs ']) .refval ∧ validrefs(str, r ' + refs0 + r0 ', fs .type, 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-class , F , [st, ty, refs, r, str] → [st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)], mkclasstype(class0), r ' + refs0 + r0 ', r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)], mkclasstype(class0), r ' + refs0 + r0 ', r0, str)]]