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Proof step 32 from proof validrefs-contains-null (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
acc + jvmref ' = r0 ' + refs, st[r -- i '] = refval(r0), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, acc + jvmref ' + refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str, refs0, ty, st. validrefs(str, acc + jvmref ' + refs0, ty, st) → validrefs(str, r0 ' + refs, ty, st) ∧ refs0 = [] ⊦ r = jvmref, validrefs(str, (r ' + acc) + jvmref ', ty, st) ∧ refs0 = [], jvmref ≠ r0 ∧ ¬ jvmref ∈ refs, ¬ r0 ∈ acc ∧ r0 ≠ jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPFORWARD : ⊦ refs + r ' = refs0 → r ∈ refs0])]]