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Proof step 12 from proof compatstatic-mode (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ is_referencevalue(val) → (compat(str, val, ty, st) ↔ okval(val, ty))
Proof step 11:
st[jvmref -- mkfs(class0, ty, fieldvar) '] = refval(r) ∧ is_referencevalue(st[jvmref -- mkfs(class0, ty, fieldvar) ']), class∃(str, class), jvmref -- mkfs(class0, ty, fieldvar) ' ∈ st[_mode, val], initdone(class, st), mkfs(class0, ty, fieldvar) ' ∈ statfields(class), jvmref ∈ st[_mode, val], okval(st[jvmref -- mkfs(class0, ty, fieldvar) '], ty), jvmref -- mkfs(class0, ty, fieldvar) ' ∈ st, jvmref ∈ st, ∀ 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]), is_referencevalue(st[jvmref -- mkfs(class0, ty, fieldvar) ']) ∧ 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) ⊦ ty = void_type, compat(str, st[jvmref -- mkfs(class0, ty, fieldvar) '], ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[jvmref -- mkfs(class0, ty, fieldvar) '], r] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[jvmref -- mkfs(class0, ty, fieldvar) '], r)]]