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Proof step 168 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) → 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 167:
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) ∨ tdname+∃(str, ty0 .jtelemtype .class), ¬ has_classtype(ty0) ∨ class∃(str, ty0 .jtelemtype .class) ∨ interface∃(str, ty0 .jtelemtype .class) ∨ is_predefined_class(ty0 .jtelemtype .class) → is_arraytype(typeval(mkarraytype(ty0)) .type) ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j0. ¬ j0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j0 → compat(str, st[r0 -- j0 '], typeval(mkarraytype(ty0)) .type .type, st)) ⊦ 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]