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Proof step 120 from proof compat-addobj (previous step)

st[r0 -- _type] = typeval(mkclasstype(class0)), r0 -- mkfs(class1, ty, fieldvar) ' ∈ st, class+∃(str, class0), is_predefined_class(class), newref(r, st), compatmode(str, st), compatstatic(str, st), r0 -- _type ∈ st, r0 ∈ st, mkfs(class1, ty, fieldvar) ' ∈ instfields(class0), compat(str, st[r0 -- mkfs(class1, ty, fieldvar) '], ty, st) ⊦ r = jvmref, r0 = jvmref, okval(st[r0 -- mkfs(class1, ty, fieldvar) '], ty) ∧ ( is_referencevalue(st[r0 -- mkfs(class1, ty, fieldvar) ']) ∧ st[r0 -- mkfs(class1, ty, fieldvar) '] .refval ≠ jvmref → st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type ∈ addobj(r, class, [], st) ∧ is_typevalue(addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) ∧ is_reftype((addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) .type) ∧ ( has_classtype((addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) .type) → class∃(str, (addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) .type .jtelemtype .class) ∨ interface∃(str, (addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) .type .jtelemtype .class) ∨ is_predefined_class((addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) .type .jtelemtype .class)) ∧ ( is_classtype((addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) .type) → class+∃(str, (addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) .type .class)) ∧ is_subtype(str, (addobj(r, class, [], st)[st[r0 -- mkfs(class1, ty, fieldvar) '] .refval -- _type]) .type, ty))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ 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, st[r0 -- mkfs(class1, ty, fieldvar) '], str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ asgcomp(str, val, ty, st) ↔ ¬ is_referencevalue(val) ∨ val .refval = jvmref ∨ is_subtype (str, st[val .refval -- _type] .type, ty)], [CSIMPSEQ : ⊦ rk ∈ st → rk ∈ addobj(r, class1, fis, st)], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ r0 ∈ st ∧ newref(r, st) → (addobj(r, class1, fis, st) [r0 -- sk ] ) = st[r0 -- sk]], [CSIMPSEQ : ⊦ ¬ is_typevalue(val) → val .type = void_type], [CSIMPSEQ : ⊦ ¬ is_reftype(void_type)], [CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)])], [EXTRATERMS : (st, ty, st[r0 -- mkfs(class1, ty, fieldvar) '], str)]]