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Proof step 165 from proof compat-addobj (previous step)

st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(i), r0 ∈ st, r0 -- _type ∈ st, compatstatic(str, st), compatmode(str, st), newref(r, st), is_predefined_class(class), ¬ has_classtype(ty0) ∨ class∃(str, ty0 .jtelemtype .class) ∨ interface∃(str, ty0 .jtelemtype .class) ∨ is_predefined_class(ty0 .jtelemtype .class) → r0 -- _length ∈ st ∧ 0 ≤ i ∧ is_arrayref(r0, i, st) ∧ (∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → compat(str, st[r0 -- j0 '], ty0, st)), ¬ has_classtype(ty0) ∨ tdname+∃(str, ty0 .jtelemtype .class) ⊦ r0 = jvmref, r = jvmref, (0 ≤ j ∧ j < i → compat(str, st[r0 -- j '], ty0, addobj(r, class, [], st))) ∧ is_arrayref(r0, i, addobj(r, class, [], st)) ∧ ¬ i < 0 ∧ r0 -- _length ∈ addobj(r, class, [], st)

User applied rule case distinction

And obtained the following new goals

Proof step 164:
r0 -- _length ∈ st ∧ 0 ≤ i ∧ is_arrayref(r0, i, st) ∧ (∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → compat(str, st[r0 -- j0 '], ty0, st)), st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(i), r0 ∈ st, r0 -- _type ∈ st, compatstatic(str, st), compatmode(str, st), newref(r, st), is_predefined_class(class), ¬ has_classtype(ty0) ∨ tdname+∃(str, ty0 .jtelemtype .class) ⊦ r0 = jvmref, r = jvmref, (0 ≤ j ∧ j < i → compat(str, st[r0 -- j '], ty0, addobj(r, class, [], st))) ∧ is_arrayref(r0, i, addobj(r, class, [], st)) ∧ ¬ i < 0 ∧ r0 -- _length ∈ addobj(r, class, [], st)

Rule argument

[CASEDARG : pos: left 9, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)])]]