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Proof step 83 from proof compat-addobj (previous step)

okval(st[jvmref -- mkfs(class1, ty, fieldvar) '], ty), jvmref ∈ st, mkfs(class1, ty, fieldvar) ' ∈ statfields(class0), compatrefs(str, st), compatmode(str, st), newref(r, st), is_predefined_class(class), initdone(class0, st), jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st, is_referencevalue(st[jvmref -- mkfs(class1, ty, fieldvar) ']), ∀ sk. sk ∈ statfields(class0) → jvmref -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[jvmref -- sk], sk .fs .type, st), class∃(str, class0) ∨ interface∃(str, class0), st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval ≠ jvmref → st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval -- _type ∈ st ∧ is_typevalue(st[st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) ∧ is_reftype(st[st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval -- _type] .type) ∧ ( has_classtype(st[st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval -- _type] .type) → tdname+∃(str, st[st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval -- _type] .type .jtelemtype .class)) ∧ ( is_classtype(st[st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval -- _type] .type) → class+∃(str, st[st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval -- _type] .type .class)) ∧ is_subtype(str, st[st[jvmref -- mkfs(class1, ty, fieldvar) '] .refval -- _type] .type, ty) ⊦ compat(str, st[jvmref -- mkfs(class1, ty, fieldvar) '], ty, st[r -- _type, typeval(mkclasstype(class))])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 82:
st[jvmref -- mkfs(class1, ty, fieldvar) '] = refval(r0), okval(st[jvmref -- mkfs(class1, ty, fieldvar) '], ty), jvmref ∈ st, mkfs(class1, ty, fieldvar) ' ∈ statfields(class0), compatrefs(str, st), compatmode(str, st), newref(r, st), is_predefined_class(class), initdone(class0, st), jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st, is_referencevalue(st[jvmref -- mkfs(class1, ty, fieldvar) ']), ∀ sk. sk ∈ statfields(class0) → jvmref -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[jvmref -- sk], sk .fs .type, st), class∃(str, class0) ∨ interface∃(str, class0), r0 ≠ jvmref → r0 -- _type ∈ st ∧ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ∧ (has_classtype(st[r0 -- _type] .type) → tdname+∃(str, st[r0 -- _type] .type .jtelemtype .class)) ∧ (is_classtype(st[r0 -- _type] .type) → class+∃(str, st[r0 -- _type] .type .class)) ∧ is_subtype(str, st[r0 -- _type] .type, ty) ⊦ compat(str, st[jvmref -- mkfs(class1, ty, fieldvar) '], ty, st[r -- _type, typeval(mkclasstype(class))])

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[jvmref -- mkfs(class1, ty, fieldvar) '], r0] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[jvmref -- mkfs(class1, ty, fieldvar) '], r0)]]