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Proof step 10 from proof okarray-onlymod (previous step)

st[r -- _type] = typeval(mkarraytype(ty0)), j < st[r -- _length] .intval, onlyModified(r0, st, st0), r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), is_arrayref(r, st[r -- _length] .intval, st0), r ∈ st, 0 ≤ st[r -- _length] .intval, 0 ≤ j, 0 < st[r -- _length] .intval, okval(st[r -- j '], ty), ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = r0, r = jvmref, okval(st0[r -- j '], ty)

User applied rule cut formula

And obtained the following new goals

Proof step 9:
st[r -- _type] = typeval(mkarraytype(ty0)), j < st[r -- _length] .intval, onlyModified(r0, st, st0), r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), is_arrayref(r, st[r -- _length] .intval, st0), r ∈ st, 0 ≤ st[r -- _length] .intval, 0 ≤ j, 0 < st[r -- _length] .intval, okval(st[r -- j '], ty), ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ st[r -- j '] = st0[r -- j '], r = r0, r = jvmref, okval(st0[r -- j '], ty)

Rule argument

[fma-arg: st[r -- j '] = st0[r -- j ']]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (st[r -- j '] = st0[r -- j '])]]