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Proof step 169 from proof compat-addobj (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 139:
⊦ compatarray(str, r, st) ↔ is_arraytype(st[r -- _type] .type) ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → compat(str, st[r -- j '], st[r -- _type] .type .type, st))
Proof step 168:
st[r0 -- _type] = typeval(mkarraytype(ty0)), is_predefined_class(class), newref(r, st), compatmode(str, st), compatstatic(str, st), r0 -- _type ∈ st, r0 ∈ st, ¬ has_classtype(ty0) ∨ class∃(str, ty0 .jtelemtype .class) ∨ interface∃(str, ty0 .jtelemtype .class) ∨ is_predefined_class(ty0 .jtelemtype .class) → is_arraytype(st[r0 -- _type] .type) ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → compat(str, st[r0 -- j '], st[r0 -- _type] .type .type, st)), ¬ has_classtype(ty0) ∨ tdname+∃(str, ty0 .jtelemtype .class) ⊦ r = jvmref, r0 = jvmref, (0 ≤ j ∧ j < st[r0 -- _length] .intval → compat(str, st[r0 -- j '], ty0, addobj(r, class, [], st))) ∧ is_arrayref(r0, st[r0 -- _length] .intval, addobj(r, class, [], st)) ∧ ¬ st[r0 -- _length] .intval < 0 ∧ is_integervalue(st[r0 -- _length]) ∧ r0 -- _length ∈ addobj(r, class, [], st)

Rule argument

[crewrite-arg: array-compat, F, [st, r, str] → [st, r0, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, str)]]