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Proof step 10 from proof compatstatic-mode (previous step)

st[jvmref -- mkfs(class0, ty, fieldvar) '] = refval(r), is_reftype(ty), jvmref ∈ st[_mode, val], mkfs(class0, ty, fieldvar) ' ∈ statfields(class), initdone(class, st), jvmref -- mkfs(class0, ty, fieldvar) ' ∈ st[_mode, val], class∃(str, class), jvmref ∈ st, jvmref -- mkfs(class0, ty, fieldvar) ' ∈ st, r ≠ jvmref → r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ is_reftype(st[r -- _type] .type) ∧ (has_classtype(st[r -- _type] .type) → tdname+∃(str, st[r -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[r -- _type] .type) → class+∃(str, st[r -- _type] .type .class)) ∧ is_subtype(str, st[r -- _type] .type, ty), ∀ sk. sk ∈ statfields(class) → jvmref -- sk ∈ st[_mode, val] ∧ is_fskey(sk) ∧ compat(str, st[_mode, val][jvmref -- sk], sk .fs .type, st[_mode, val]) ⊦ ty = void_type, compat(str, refval(r), ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ compat(str, val, ty, st) ↔ okval(val, ty) ∧ ( is_referencevalue(val) ∧ val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ is_reftype(st[val .refval -- _type] .type) ∧ (has_classtype(st[val .refval -- _type] .type) → tdname+∃(str, st[val .refval -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[val .refval -- _type] .type) → class+∃(str, st[val .refval -- _type] .type .class)) ∧ asgcomp(str, val, ty, st))

Rule argument

[crewrite-arg: value-compat , F , [st, ty, val, str] → [st, ty, refval(r), str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ okval(refval(r), ty) ↔ ty = void_type ∨ is_reftype(ty)], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)], [CSIMPSEQ : ⊦ asgcomp(str, val, ty, st) ↔ ¬ is_referencevalue(val) ∨ val .refval = jvmref ∨ is_subtype (str, st[val .refval -- _type] .type, ty)])], [EXTRATERMS : (st, ty, refval(r), str)]]