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Proof step 6 from proof ubifs-cons-ri-inj (previous step)

ri[key] = ri[key0], fo.inodes?, ro.inodes?, key ∈ ri, key0 ∈ ri, fo ⊆ dom fi, ro ⊆ dom 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), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]) ⊦ key = key0, dups(log), inodekey(0) ∈ ri

User applied rule all left

And obtained the following new goals

Proof step 7:
ri[key] = ri[key0], ro.inodes?, fo.inodes?, key0 ∈ ri, key ∈ ri, ro ⊆ dom ri, fo ⊆ dom fi, key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]), ∀ key. 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]]) ⊦ key = key0, dups(log), inodekey(0) ∈ ri

Rule argument

pos: left 8 terms: key abort: F discard: F computed: T

Additional information

Used terms: key