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Proof step 68 from proof validrefs-put-last (previous step)

is_array(str, r, st), validrefs(str, (r ' + acc) + r0 ', ty, st[r0 -- sk, val]), st[r -- _type] .type ≤ ty, ∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ sk = _type, r0 = r, r = jvmref, r0 ∈ acc, junkref(str, r, st), validrefs(str, (r ' + acc) + r0 ', ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 67:
is_array(str, r, st[r0 -- sk, val]) ∧ (st[r0 -- sk, val][r -- _type]) .type ≤ ty, is_array(str, r, st), acc + r0 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < (st[r0 -- sk, val][r -- _length]) .intval ∧ is_referencevalue(st[r0 -- sk, val][r -- i ']) ∧ (acc + r0 ') .first = (st[r0 -- sk, val][r -- i ']) .refval ∧ validrefs(str, acc + r0 ', (st[r0 -- sk, val][r -- _type]) .type .type, st[r0 -- sk, val])), st[r -- _type] .type ≤ ty, ∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ sk = _type, r0 = r, r = jvmref, r0 ∈ acc, junkref(str, r, st), validrefs(str, (r ' + acc) + r0 ', ty, st)

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st[r0 -- sk, val], ty, acc + r0 ', r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st[r0 -- sk, val], ty, acc + r0 ', r, str)]]