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Proof step 22 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 -- _length] .intval, 0 < st[r -- _length] .intval, is_reftype(st[r -- _type] .type), ∀ 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 '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ junkref(str, r, st) → ¬ validref(str, r, ty, st)
Proof step 21:
¬ junkref(str, r, st), 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 -- _length] .intval, 0 < st[r -- _length] .intval, is_reftype(st[r -- _type] .type), ∀ 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 '])

Rule argument

[crewrite-arg: validref-junkref , F , [st, ty, r, str] → [st, mkarraytype(ty), r, str] ]

Additional information

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