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Proof step 8 from proof compatarray-abstract (previous step)

st[r -- _type] .type = mkarraytype(abstract_type), 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)) ⊦ r = jvmref, st[r -- _length] .intval = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
st[r -- _type] .type = mkarraytype(abstract_type), 0 < st[r -- _length] .intval, r ∈ st, is_integervalue(st[r -- _length]), r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → compat(str, st[r -- j '], abstract_type, st) ⊦ st[r -- _length] .intval = 0, r = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)])]]