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Proof step 22 from proof sortedchars-no-dups (previous step)

dups(s→l("!#$%&()*+-")) ∨ ( dups(s→l("./0123456789:<=>?@")) ∨ ( dups(s→l("ABCDEFGHIJKLM")) ∨ dups(s→l("NOPQRSTUVWXYZ") + s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ∨ filter(s→l("ABCDEFGHIJKLM"), s→l("NOPQRSTUVWXYZ") + s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ≠ []) ∨ filter(s→l("./0123456789:<=>?@"), s→l("ABCDEFGHIJKLM") + s→l("NOPQRSTUVWXYZ") + s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ≠ []) ∨ filter (s→l("!#$%&()*+-"), s→l("./0123456789:<=>?@") + s→l("ABCDEFGHIJKLM") + s→l("NOPQRSTUVWXYZ") + s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ≠ [] ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ dups(chars + chars0) ↔ dups(chars) ∨ dups(chars0) ∨ filter(chars, chars0) ≠ []
Proof step 24:
dups(s→l("!#$%&()*+-")) ∨ ( dups(s→l("./0123456789:<=>?@")) ∨ ( dups(s→l("ABCDEFGHIJKLM")) ∨ ( dups(s→l("NOPQRSTUVWXYZ")) ∨ dups(s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ∨ filter(s→l("NOPQRSTUVWXYZ"), s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ≠ []) ∨ filter(s→l("ABCDEFGHIJKLM"), s→l("NOPQRSTUVWXYZ") + s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ≠ []) ∨ filter(s→l("./0123456789:<=>?@"), s→l("ABCDEFGHIJKLM") + s→l("NOPQRSTUVWXYZ") + s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ≠ []) ∨ filter (s→l("!#$%&()*+-"), s→l("./0123456789:<=>?@") + s→l("ABCDEFGHIJKLM") + s→l("NOPQRSTUVWXYZ") + s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~")) ≠ [] ⊦

Rule argument

spec: list-set inst: charlist name: dups-app seq: ⊦ dups(chars + chars0) ↔ dups(chars) ∨ dups(chars0) ∨ filter(chars, chars0) ≠ [] subst: [chars0, chars] → [s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~"), s→l("NOPQRSTUVWXYZ")] flags: rewrite

Additional information

Used terms: s→l("[]^_abcdefghi") + s→l("jklmnopqrs") + s→l("tuvwxyz|~"), s→l("NOPQRSTUVWXYZ")