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Proof step 34 from proof getarray-subset (previous step)

st[r -- _length] = intval(i0), st0[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _length] = intval(i), r -- _type ∈ st, n < i→n(i), r -- _type ∈ st0, ty0 ≤ ty, r -- _length ∈ st0, r ∈ st0, 0 < i, is_arrayref(r, i, st0), r ∈ st, n < # getarray(r, st0), st ⊆ st0, is_arrayref(r, i0, st), 0 ≤ i0, is_integervalue(st[r -- _length]), r -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → oktype(st[r -- j '], ty, st), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st0) ⊦ r = jvmref, noval = st0[r -- n→i(n) '], i = 0, getarray(r, st0) = [], r -- n→i(n) ' ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
st0[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(i0), 0 ≤ i0, r -- _length ∈ st, is_arrayref(r, i0, st), st ⊆ st0, n < # getarray(r, st0), r ∈ st, is_arrayref(r, i, st0), 0 < i, r ∈ st0, r -- _length ∈ st0, ty0 ≤ ty, r -- _type ∈ st0, n < i→n(i), r -- _type ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st0), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → oktype(st[r -- j '], ty, st) ⊦ getarray(r, st0) = [], i = 0, noval = st0[r -- n→i(n) '], r = jvmref, r -- n→i(n) ' ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j])]]