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Proof step 12 from proof disjoint-symmetric (previous step)

⊦ (∀ refs, refs0. refs = [] ∨ refs0 = [] ∨ refs .first ≠ r ∧ refs .first ≠ r0 ∨ refs0 .first ≠ r ∧ refs0 .first ≠ r0 ∨ refs .first = refs0 .first ∨ refs .last ≠ refs0 .last ∨ refs .last = jvmref ∨ ¬ validrefs(str, refs, st[refs .first -- _type] .type, st) ∨ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st)) ↔ ¬ (∃ refs1, refs2. refs1 ≠ [] ∧ refs2 ≠ [] ∧ refs1 .first ∈ r0 ' + r ' ∧ refs2 .first ∈ r0 ' + 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 11:
⊦ (∀ refs, refs0. refs = [] ∨ refs0 = [] ∨ refs .first ≠ r ∧ refs .first ≠ r0 ∨ refs0 .first ≠ r ∧ refs0 .first ≠ r0 ∨ refs .first = refs0 .first ∨ refs .last ≠ refs0 .last ∨ refs .last = jvmref ∨ ¬ validrefs(str, refs, st[refs .first -- _type] .type, st) ∨ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st)) ↔ (∀ refs, refs0. refs = [] ∨ refs0 = [] ∨ refs .first ≠ r0 ∧ refs .first ≠ r ∨ refs0 .first ≠ r0 ∧ refs0 .first ≠ r ∨ refs .first = refs0 .first ∨ refs .last ≠ refs0 .last ∨ refs .last = jvmref ∨ ¬ validrefs(str, refs, st[refs .first -- _type] .type, st) ∨ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st))

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)])]]