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Proof step 5 from proof nodups-new-nodups (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 6:
new(ax, fs), adr = adr ∨ adr ∈ log0 → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]), ∀ adr0. adr0 ∈ log0 → adr0 ∈ fs ∧ node-cons(fs[adr0].key, fs[adr0]), ∀ ax0, fs0. dups(log0 + ax0) ∧ new(ax0, fs0) ∧ (∀ adr. adr ∈ log0 → adr ∈ fs0 ∧ node-cons(fs0[adr].key, fs0[adr])) → dups(ax0), adr ∈ ax ∨ dups(log0 + ax) ⊦ dups(log0), dups(ax), adr ∈ log0

Rule argument

pos: left 3 terms: adr abort: F discard: F computed: T

Additional information

Used terms: adr