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Proof step 8 from proof validreflist-getarray-less-02 (previous step)

validreflist(str, getarray(r, j + 1, i1, st), ty, st), 0 ≤ i1, j + i1 < st[r -- _length] .intval, 0 ≤ j, is_reftype(ty), validref(str, r, mkarraytype(ty), st), ∀ j, st, r, str, ty, i0. i→n(i0) < i→n(i1 + 1) → ( is_reftype(ty) ∧ validrefnotnull(str, r, mkarraytype(ty), st) ∧ j + i0 ≤ st[r -- _length] .intval ∧ 0 ≤ i0 ∧ 0 ≤ j → r = jvmref ∨ validreflist(str, getarray(r, j, i0, st), ty, st)) ⊦ r = jvmref, is_referencevalue(st[r -- j ']) ∧ validref(str, st[r -- j '] .refval, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ r ≠ jvmref ∧ ¬ validref(str, st0[r -- i '] .refval, ty, st0) ∧ 0 ≤ i ∧ i < st0[r -- _length] .intval → ¬ validref(str, r, mkarraytype(ty), st0)
Proof step 7:
⊦ ¬ is_referencevalue(st[r -- i ']) ∧ is_reftype(ty) ∧ r ≠ jvmref ∧ 0 ≤ i ∧ i < st[r -- _length] .intval → ¬ validref(str, r, mkarraytype(ty), st)

Rule argument

[crewrite-arg: validref-forward-array-01 , F , [r, str, st0, i, ty] → [r, str, st, j, ty] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (r, str, st, j, ty)]]