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Proof step 178 from proof compat-addobj (previous step)

st[r0 -- _type] = typeval(ty), is_predefined_class(class), newref(r, st), compatmode(str, st), compatstatic(str, st), ∀ r. r ≠ jvmref ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) → (is_classtype(st[r -- _type] .type) ∧ class+∃(str, st[r -- _type] .type .class) → compatobj(str, r, st)) ∧ ( is_arraytype(st[r -- _type] .type) ∧ (¬ has_classtype(st[r -- _type] .type) ∨ tdname+∃(str, st[r -- _type] .type .jtelemtype .class)) → compatarray(str, r, st)), r0 -- _type ∈ st, r0 ∈ st ⊦ r = jvmref, r0 = jvmref, (is_classtype(ty) ∧ class+∃(str, ty .class) → compatobj(str, r0, addobj(r, class, [], st))) ∧ (is_arraytype(ty) ∧ (¬ has_classtype(ty) ∨ tdname+∃(str, ty .type .jtelemtype .class)) → compatarray(str, r0, addobj(r, class, [], st)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 177:
st[r0 -- _type] = typeval(ty), is_predefined_class(class), newref(r, st), compatmode(str, st), compatstatic(str, st), r0 -- _type ∈ st, r0 ∈ st, ∀ r1. r1 ≠ jvmref ∧ r1 -- _type ∈ st ∧ is_typevalue(st[r1 -- _type]) → (is_classtype(st[r1 -- _type] .type) ∧ class+∃(str, st[r1 -- _type] .type .class) → compatobj(str, r1, st)) ∧ ( is_arraytype(st[r1 -- _type] .type) ∧ ( ¬ has_classtype(st[r1 -- _type] .type) ∨ class∃(str, st[r1 -- _type] .type .type .jtelemtype .class) ∨ interface∃(str, st[r1 -- _type] .type .type .jtelemtype .class) ∨ is_predefined_class(st[r1 -- _type] .type .type .jtelemtype .class)) → compatarray(str, r1, st)) ⊦ r = jvmref, r0 = jvmref, (is_classtype(ty) ∧ class+∃(str, ty .class) → compatobj(str, r0, addobj(r, class, [], st))) ∧ (is_arraytype(ty) ∧ (¬ has_classtype(ty) ∨ tdname+∃(str, ty .type .jtelemtype .class)) → compatarray(str, r0, addobj(r, class, [], st)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)], [CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ is_arraytype(ty) → ty .jtelemtype = ty .type .jtelemtype])]]