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Proof step 52 from proof validrefs-junkrefs-01 (previous step)

st[r -- i '] = refval(r0), acc + refs0 = r0 ' + refs, 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, junkrefs(str, acc + refs0, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), ∀ str, refs0, ty, st. junkrefs(str, acc + refs0, ty, st) → junkrefs(str, acc, ty, st) ∨ validrefs(str, acc, ty, st) ⊦ acc + refs0 = [], r = jvmref, validrefs(str, r ' + acc, ty, st), junkrefs(str, r ' + acc, ty, st), ¬ r0 ∈ acc ∧ ¬ r0 ∈ refs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
acc + refs0 = r0 ' + refs, st[r -- i '] = refval(r0), is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, acc + refs0, st[r -- _type] .type .type, st), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str, refs0, ty, st. junkrefs(str, acc + refs0, ty, st) → junkrefs(str, acc, ty, st) ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, acc + refs0 = [], junkrefs(str, r ' + acc, ty, st), validrefs(str, r ' + acc, ty, st), ¬ r0 ∈ acc ∧ ¬ r0 ∈ refs0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0])]]