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Proof step 15 from proof okarray-putbar-other (previous step)

st[r -- _length] = intval(i0), st[r -- _type] = typeval(ty0), r -- _type ∈ st, r -- _length ∈ st, r ∈ st, 0 ≤ i0 ⊦ is_arraytype(ty0) ∧ ty0 .type ≤ ty ∧ is_arrayref(r, i0, putByteArray(bytes, r1, i, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty)) ↔ ty0 ≤ mkarraytype(ty) ∧ is_arrayref(r, i0, st) ∧ (∀ j. 0 ≤ j ∧ j < i0 → okval(st[r -- j '], ty)), r = jvmref, r = r1

User applied rule case distinction

And obtained the following new goals

Proof step 13:
is_arraytype(ty0) ∧ ty0 .type ≤ ty ∧ is_arrayref(r, i0, putByteArray(bytes, r1, i, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty)), st[r -- _length] = intval(i0), st[r -- _type] = typeval(ty0), r -- _type ∈ st, r -- _length ∈ st, r ∈ st, 0 ≤ i0 ⊦ ty0 ≤ mkarraytype(ty) ∧ is_arrayref(r, i0, st) ∧ (∀ j. 0 ≤ j ∧ j < i0 → okval(st[r -- j '], ty)), r = jvmref, r = r1
Proof step 14:
ty0 ≤ mkarraytype(ty) ∧ is_arrayref(r, i0, st) ∧ (∀ j. 0 ≤ j ∧ j < i0 → okval(st[r -- j '], ty)), st[r -- _length] = intval(i0), st[r -- _type] = typeval(ty0), r -- _type ∈ st, r -- _length ∈ st, r ∈ st, 0 ≤ i0 ⊦ is_arraytype(ty0) ∧ ty0 .type ≤ ty ∧ is_arrayref(r, i0, putByteArray(bytes, r1, i, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty)), r = jvmref, r = r1

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]