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Proof step 32 from proof inv-replay (previous step)

replay-log(log0, fs0, fi0 ⊖ fo0) = (ri \ ro) \ datakeys(ro, ri), fo0.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), node-closed(fs0[ri[key]], ri, fs0, ro), orphans-cons(fs0, ri, ro), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-closed(ri, fs0, ro), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi0), key ∈ ri, ri[key] ∈ fs0, ro ⊆ dom ri, fo0 ⊆ dom fi0, ¬ key.data? ∨ ¬ inodekey(key.ino) ∈ ro ⊦ dups(log0), inodekey(0) ∈ ri, key ∈ ro, key ∈ ri ∧ ¬ key ∈ ro ∧ ¬ key.data?, (key.data? ∧ inodekey(key.ino) ∈ ro ⊃ (∅)[key];ri[key]) ∈ fs0 ∧ node-closed(fs0[(key.data? ∧ inodekey(key.ino) ∈ ro ⊃ (∅)[key];ri[key])], replay-log(log0, fs0, fi0 ⊖ fo0), fs0, ∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
replay-log(log0, fs0, fi0 ⊖ fo0) = (ri \ ro) \ datakeys(ro, ri), fo0.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), node-closed(fs0[ri[datakey(ino, n)]], ri, fs0, ro), orphans-cons(fs0, ri, ro), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-closed(ri, fs0, ro), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi0), datakey(ino, n) ∈ ri, ri[datakey(ino, n)] ∈ fs0, ro ⊆ dom ri, fo0 ⊆ dom fi0 ⊦ dups(log0), node-closed(fs0[ri[datakey(ino, n)]], replay-log(log0, fs0, fi0 ⊖ fo0), fs0, ∅), inodekey(0) ∈ ri, inodekey(ino) ∈ ro

Rule argument

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s)