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Proof step 128 from proof compat-put (previous step)

st[r0 -- _type] = typeval(ty0), r0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 -- _type ∈ st[r -- mkfs(class, ty, fieldvar) ', val], compatmode(str, st), compatstatic(str, st), compatrefs(str, st), compat(str, val, ty, st) ⊦ mkfs(class, ty, fieldvar) ' = _length, ty = void_type, r0 = jvmref, (is_classtype(ty0) ∧ class+∃(str, ty0 .class) → compatobj(str, r0, st[r -- mkfs(class, ty, fieldvar) ', val])) ∧ ( is_arraytype(ty0) ∧ (¬ has_classtype(ty0) ∨ tdname+∃(str, ty0 .type .jtelemtype .class)) → compatarray(str, r0, st[r -- mkfs(class, ty, fieldvar) ', val]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
⊦ compatrefs(str, st) ↔ (∀ r. r ≠ jvmref ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) → (is_classtype(st[r -- _type] .type) ∧ class+∃(str, st[r -- _type] .type .class) → compatobj(str, r, st)) ∧ ( is_arraytype(st[r -- _type] .type) ∧ (¬ has_classtype(st[r -- _type] .type) ∨ tdname+∃(str, st[r -- _type] .type .jtelemtype .class)) → compatarray(str, r, st)))
Proof step 127:
st[r0 -- _type] = typeval(ty0), r0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 -- _type ∈ st[r -- mkfs(class, ty, fieldvar) ', val], compatmode(str, st), compatstatic(str, st), ∀ r. r ≠ jvmref ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) → (is_classtype(st[r -- _type] .type) ∧ class+∃(str, st[r -- _type] .type .class) → compatobj(str, r, st)) ∧ ( is_arraytype(st[r -- _type] .type) ∧ (¬ has_classtype(st[r -- _type] .type) ∨ tdname+∃(str, st[r -- _type] .type .jtelemtype .class)) → compatarray(str, r, st)), compat(str, val, ty, st) ⊦ mkfs(class, ty, fieldvar) ' = _length, ty = void_type, r0 = jvmref, (is_classtype(ty0) ∧ class+∃(str, ty0 .class) → compatobj(str, r0, st[r -- mkfs(class, ty, fieldvar) ', val])) ∧ ( is_arraytype(ty0) ∧ (¬ has_classtype(ty0) ∨ tdname+∃(str, ty0 .type .jtelemtype .class)) → compatarray(str, r0, st[r -- mkfs(class, ty, fieldvar) ', val]))

Rule argument

[crewrite-arg: refs-compat, F, [st, str] → [st, str]]

Additional information

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