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Proof step 28 from proof okarray-put-okval (previous step)

st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st, ty0 ≤ ty, r -- _type ∈ st, okval(val, ty), is_arrayref(r, i0, st), r -- _length ∈ st, 0 ≤ i0, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, j = i, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st[r -- i ', val] ∧ is_typevalue(st[r -- i ', val][refval(r) .refval -- _type]) ∧ (st[r -- i ', val][refval(r) .refval -- _type]) .type ≤ mkarraytype(ty)) ∧ (0 ≤ j ∧ j < i0 → okval(st[r -- i ', val][r -- j '], ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(i0), 0 ≤ i0, r -- _length ∈ st, is_arrayref(r, i0, st), okval(val, ty), r -- _type ∈ st, ty0 ≤ ty, r ∈ st, j < i0, 0 ≤ j, 0 < i0, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → okval(st[r -- j0 '], ty) ⊦ j = i, r = jvmref, okval(st[r -- i ', val][r -- j '], ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ (st[r -- i ', val][r0 -- _type]) = st[r0 -- _type]], [CSIMPSEQ : ⊦ r -- _type ∈ st[r0 -- i ', val0] ↔ r -- _type ∈ st], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]