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Proof step 67 from proof validrefs-put-last (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
(acc + r0 ') .first = st[r -- i '] .refval, is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, acc + r0 ', st[r -- _type] .type .type, st[r0 -- sk, val]), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))])]]