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Proof step 82 from proof validrefs-del-junkrefs (previous step)

is_array(str, r0, st -- r) ∧ (st -- r)[r0 -- _type] .type ≤ ty, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, (r1 ' + acc) + r ' ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st -- r)[r0 -- _length] .intval ∧ is_referencevalue((st -- r)[r0 -- i ']) ∧ ((r1 ' + acc) + r ') .first = (st -- r)[r0 -- i '] .refval ∧ junkrefs(str, (r1 ' + acc) + r ', (st -- r)[r0 -- _type] .type .type, st -- r)), ∀ st, r0, ty, str, r. st[r0 -- _type] .type ≤ ty ∧ junkrefs(str, (r0 ' + acc) + r ', ty, st -- r) → r = r0 ∨ junkref(str, r0, st) ∨ r ∈ acc ∨ validrefs(str, r0 ' + acc + r ', ty, st) ⊦ r = r0, r = r1, r0 = jvmref, junkref(str, r0, st), r ∈ acc, validrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
0 < st[r0 -- _length] .intval, 0 ≤ i, junkrefs(str, (st[r0 -- i '] .refval ' + acc) + r ', st[r0 -- _type] .type .type, st -- r), is_referencevalue(st[r0 -- i ']), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), ∀ st, r0, ty, str, r. st[r0 -- _type] .type ≤ ty ∧ junkrefs(str, (r0 ' + acc) + r ', ty, st -- r) → r = r0 ∨ junkref(str, r0, st) ∨ r ∈ acc ∨ validrefs(str, r0 ' + acc + r ', ty, st) ⊦ r0 = jvmref, r = st[r0 -- i '] .refval, r = r0, validrefs(str, r0 ' + (st[r0 -- i '] .refval ' + acc) + r ', ty, st), r ∈ acc, junkref(str, r0, st)

Rule argument

[emptyarg]

Additional information

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