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Proof step 22 from proof replay-safe-gc-copy (previous step)

# ax0 = # kx1, ro.inodes?, new(ax0, fs), orphans-cons(fs, ri, ro), ri-closed(ri, fs, ro), key ∈ ri, kx1.toSet ⊆ dom ri, ∀ kx0, ro0, fs0, ri0. # kx1 = # kx0 ∧ ro0.inodes? ∧ new(ax0, fs0) ∧ orphans-cons(fs0, ri0, ro0) ∧ ri-closed(ri0, fs0, ro0) ∧ ri-cons(ri0, fs0) ∧ kx0.toSet ⊆ dom ri0 → dups(kx0) ∨ replay-safe(ax0, fs0[ax0, fs0[ri0[kx0]]], ri0 ⊖ ro0), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(ax0), dups(kx1), node-cons(key, fs[ri[key]]), adr ∈ ax0, adr ∈ fs, key ∈ kx1

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: key abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ key-cons(key, nd) → node-cons(key, nd); (ss) Used terms: key