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Proof step 36 from proof getarray-subset (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
⊦ 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 35:
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, st[r -- _length] .intval, st), 0 ≤ st[r -- _length] .intval, is_integervalue(st[r -- _length]), r -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ 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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]