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Proof step 5 from proof ri-closed-gc-one (previous step)

key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro) ⊦ node-closed(fs[ri[key]], ri[key, adr], fs[adr, fs[ri[key]]], ro), adr ∈ fs

User applied rule all left

And obtained the following new goals

Proof step 6:
key ∈ ri, key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ node-closed(fs[ri[key]], ri[key, adr], fs[adr, fs[ri[key]]], ro), adr ∈ fs

Rule argument

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

Additional information

Used terms: key