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Proof step 7 from proof compatarray-isarray-01 (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ 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 → oktype(st[r -- j '], ty, st)), r ∈ st, r -- _length ∈ st, r -- _type ∈ st, ∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → compat(str, st[r -- i '], ty, st) ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → compat(str, st[r -- j '], ty, st)) ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ is_integervalue(st[r -- _length])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
st[r -- _type] = typeval(mkarraytype(ty)), okreftype(refval(r), mkarraytype(ty), st), is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), r ∈ st, r -- _length ∈ st, r -- _type ∈ st, j < st[r -- _length] .intval, 0 ≤ st[r -- _length] .intval, 0 ≤ j, 0 < st[r -- _length] .intval, ∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → compat(str, st[r -- i '], ty, st), ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, compat(str, st[r -- j '], ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]