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Proof step 77 from proof compat-addobj (previous step)

st[jvmref -- mkfs(class1, ty, fieldvar) '] = refval(r0), jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st, initdone(class0, st), is_predefined_class(class), newref(r, st), compatmode(str, st), compatrefs(str, st), mkfs(class1, ty, fieldvar) ' ∈ statfields(class0), jvmref ∈ st, okval(refval(r0), ty), 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), class∃(str, class0) ∨ interface∃(str, class0), ∀ sk. sk ∈ statfields(class0) → jvmref -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[jvmref -- sk], sk .fs .type, st) ⊦ r0 = r, (ty = void_type ∨ is_reftype(ty)) ∧ ( r0 ≠ jvmref → r0 -- _type ∈ st ∧ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ∧ ( has_classtype(st[r0 -- _type] .type) → class∃(str, st[r0 -- _type] .type .jtelemtype .class) ∨ interface∃(str, st[r0 -- _type] .type .jtelemtype .class) ∨ is_predefined_class(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))

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ okval(refval(r), ty) ↔ ty = void_type ∨ is_reftype(ty)], [CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)])]]