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Proof step 26 from proof validreflist-getarray-less-01 (previous step)

validreflist(str, getarray(r, j + 1, i1, st), ty, st), 0 ≤ i1, is_reftype(ty), validref(str, r, mkarraytype(ty), st), j + i1 + 1 < st[r -- _length] .intval, 0 ≤ j, ∀ 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 25:
¬ (r ≠ jvmref ∧ ¬ validref(str, st[r -- j '] .refval, ty, st) ∧ 0 ≤ j ∧ j < st[r -- _length] .intval), validreflist(str, getarray(r, j + 1, i1, st), ty, st), 0 ≤ i1, is_reftype(ty), validref(str, r, mkarraytype(ty), st), j + i1 + 1 < st[r -- _length] .intval, 0 ≤ j, ∀ 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)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, str, st, j, ty)]]