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Proof step 8 from proof to-ards-no-dups (previous step)

∀ n. dups(lax0.to-adr(n)) ↔ dups(lax0) ⊦ @(n, m, m0) ∈ lax0.to-adr(n) ∨ dups(lax0.to-adr(n)) ↔ @(m, m0) ∈ lax0 ∨ dups(lax0), dups(lax0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
dups(lax0.to-adr(n)), ∀ n0. ¬ dups(lax0.to-adr(n0)) ⊦ dups(lax0), @(m, m0) ∈ lax0, @(n, m, m0) ∈ lax0.to-adr(n)

Rule argument

Additional information

Used simplifier rules: to-adrs-in: ⊦ @(m, m0, m1) ∈ lax.to-adr(n) ↔ m = n ∧ @(m0, m1) ∈ lax;