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Proof step 17 from proof okarray-put-okval-01 (previous step)

st[r0 -- _length] = intval(j), st[r0 -- _type] = typeval(mkarraytype(ty0)), is_arrayref(r0, j, st), okval(val0, ty), r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, 0 ≤ j, r0 ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r0 -- j0 '], ty), r0 ≠ r ∨ j0 ≠ i ⊦ r0 = jvmref, is_referencevalue(refval(r0)) ∧ ( refval(r0) .refval ≠ jvmref → refval(r0) .refval -- _type ∈ st[r -- i ', val0] ∧ is_typevalue(st[r -- i ', val0][refval(r0) .refval -- _type]) ∧ (st[r -- i ', val0][refval(r0) .refval -- _type]) .type ≤ mkarraytype(ty)) ∧ is_arrayref(r0, j, st[r -- i ', val0]) ∧ (0 ≤ j0 ∧ j0 < j → okval(st[r -- i ', val0][r0 -- j0 '], ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(j), r0 ∈ st, 0 ≤ j, r0 -- _length ∈ st, ty0 ≤ ty, r0 -- _type ∈ st, okval(val0, ty), is_arrayref(r0, j, st), r0 ≠ r ∨ j0 ≠ i, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r0 -- j0 '], ty) ⊦ r0 = jvmref, is_arrayref(r0, j, st[r -- i ', val0]) ∧ (0 ≤ j0 ∧ j0 < j → okval(st[r -- i ', val0][r0 -- j0 '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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))])]]