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Proof step 44 from proof getarray-subset (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 43:
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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]