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Proof step 13 from proof validreflist-getarray-less-02 (previous step)

validrefnotnull(str, r, mkarraytype(ty), st), is_reftype(ty), 0 ≤ j, j + i1 < st[r -- _length] .intval, 0 ≤ i1, ∀ 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, validreflist(str, st[r -- j '] ' + getarray(r, j + 1, i1, st), ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ validreflist(str, val ' + vals, ty, st) ↔ is_referencevalue(val) ∧ validref(str, val .refval, ty, st) ∧ validreflist(str, vals, ty, st)
Proof step 12:
validrefnotnull(str, r, mkarraytype(ty), st), is_reftype(ty), 0 ≤ j, j + i1 < st[r -- _length] .intval, 0 ≤ i1, ∀ 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) ∧ validreflist(str, getarray(r, j + 1, i1, st), ty, st)

Rule argument

[crewrite-arg: validreflist-rec , F , [st, ty, vals, val, str] → [st, ty, getarray(r, j + 1, i1, st), st[r -- j '], str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, getarray(r, j + 1, i1, st), st[r -- j '], str)]]