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Proof step 43 from proof getarray-subset (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 42:
st0[r -- _type] .type = mkarraytype(ty0), st[r -- _type] = typeval(mkarraytype(ty)), is_arrayref(r, st0[r -- _length] .intval, st0), r ∈ st, n < # getarray(r, st0), st ⊆ st0, okarray(r, ty, st), r -- _type ∈ st, r -- _length ∈ st, n < i→n(st0[r -- _length] .intval), r -- _type ∈ st0, is_typevalue(st0[r -- _type]), is_arraytype(st0[r -- _type] .type), ty0 ≤ ty, r -- _length ∈ st0, is_integervalue(st0[r -- _length]), 0 < st0[r -- _length] .intval, r ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ st0[r -- _length] .intval ≤ j → oktype(st0[r -- j '], ty, st0) ⊦ noval = st0[r -- n→i(n) '], st0[r -- _length] .intval = 0, getarray(r, st0) = [], r = jvmref, r -- n→i(n) ' ∈ st

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st0[r -- _type] .type, ty0] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st0[r -- _type] .type, ty0)]]