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Proof step 25 from proof union-okarray (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st, ty0 ≤ ty, r -- _type ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st0 ∪ st ∧ is_typevalue((st0 ∪ st)[refval(r) .refval -- _type]) ∧ (st0 ∪ st)[refval(r) .refval -- _type] .type ≤ mkarraytype(ty)) ∧ is_arrayref(r, i, st0 ∪ st) ∧ (0 ≤ j ∧ j < i → okval((st0 ∪ st)[r -- j '], ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r -- _type ∈ st, ty0 ≤ ty, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, is_arrayref(r, i, st0 ∪ st) ∧ (0 ≤ j ∧ j < i → okval((st0 ∪ st)[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]], [CSIMPSEQ : ⊦ rk ∈ st ∪ st0 ↔ rk ∈ st ∨ rk ∈ st0], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]