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Proof step 7 from proof nodups-new-nodups (previous step)

dups(log0 + ax), new(ax, fs), node-cons(fs[adr].key, fs[adr]), adr ∈ fs, ∀ ax0, fs0. dups(log0 + ax0) ∧ new(ax0, fs0) ∧ (∀ adr. adr ∈ log0 → adr ∈ fs0 ∧ node-cons(fs0[adr].key, fs0[adr])) → dups(ax0), ∀ adr0. adr0 ∈ log0 → adr0 ∈ fs ∧ node-cons(fs[adr0].key, fs[adr0]) ⊦ dups(ax), dups(log0), adr ∈ log0

User applied rule all left

And obtained the following new goals

Proof step 8:
dups(log0 + ax), new(ax, fs), node-cons(fs[adr].key, fs[adr]), adr ∈ fs, dups(log0 + ax) ∧ new(ax, fs) ∧ (∀ adr. adr ∈ log0 → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr])) → dups(ax), ∀ adr0. adr0 ∈ log0 → adr0 ∈ fs ∧ node-cons(fs[adr0].key, fs[adr0]) ⊦ dups(log0), dups(ax), adr ∈ log0

Rule argument

pos: left 5 terms: ax, fs abort: F discard: T computed: T

Additional information

Used terms: ax, fs