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Proof step 13 from proof disjoint-newref-01 (previous step)

newref(r, st) ⊦ r = r1, r = jvmref, ∀ refs1, refs2. ¬ ( refs1 ≠ [] ∧ refs2 ≠ [] ∧ refs1 .first ∈ r1 ' + r ' ∧ refs2 .first ∈ r1 ' + r ' ∧ refs1 .first ≠ refs2 .first ∧ refs1 .last = refs2 .last ∧ refs1 .last ≠ jvmref ∧ validrefs(str, refs1, st[refs1 .first -- _type] .type, st) ∧ validrefs(str, refs2, st[refs2 .first -- _type] .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
refs0 .last = refs .last, validrefs(str, refs0, st[refs0 .first -- _type] .type, st), validrefs(str, refs, st[refs .first -- _type] .type, st), newref(r, st) ⊦ r = r1, r = jvmref, refs .last = jvmref, refs0 .first = refs .first, refs = [], refs0 = [], refs0 .first ≠ r1 ∧ refs0 .first ≠ r, refs .first ≠ r1 ∧ refs .first ≠ r

Rule argument

[emptyarg]

Additional information

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