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Proof step 30 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), 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), ro ⊆ dom ri, fo0 ⊆ dom fi0 ⊦ dups(log0), inodekey(0) ∈ ri, inodekey(0) ∈ (ri \ ro) \ datakeys(ro, ri), key ∈ ri ∧ ¬ key ∈ ro ∧ ¬ key.data?, ( (key ∈ ri → ri[key] ∈ fs0 ∧ node-closed(fs0[ri[key]], ri, fs0, ro)) → key ∈ (ri \ ro) \ datakeys(ro, ri) → ((ri \ ro) \ datakeys(ro, ri))[key] ∈ fs0 ∧ node-closed(fs0[((ri \ ro) \ datakeys(ro, ri))[key]], (ri \ ro) \ datakeys(ro, ri), fs0, ∅)) ∧ file-node-cons(fs0, (ri \ ro) \ datakeys(ro, ri)) ∧ orphans-cons(fs0, (ri \ ro) \ datakeys(ro, ri), ∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
replay-log(log0, fs0, fi0 ⊖ fo0) = (ri \ ro) \ datakeys(ro, ri), ro.inodes?, fo0.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-closed(ri, fs0, ro), ri-cons(ri, fs0), ri-inj(fi0), ri-inj(ri), fo0 ⊆ dom fi0, ro ⊆ dom ri ⊦ dups(log0), inodekey(0) ∈ ri, key ∈ ri ∧ ¬ key ∈ ro ∧ ¬ key.data?, ( ri[key] ∈ fs0 ∧ node-closed(fs0[ri[key]], ri, fs0, ro) → key ∈ ri ∧ ¬ key ∈ ro ∧ (¬ key.data? ∨ ¬ inodekey(key.ino) ∈ ro) → (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, ∅)) ∧ file-node-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0)) ∧ orphans-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0), ∅)

Rule argument

Additional information

Used simplifier rules: at-diff-ri: ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]);% ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key]; (s)%⊦ key ∈ datakeys(ks, ri) ↔ key ∈ ri ∧ key.data? ∧ inodekey(key.ino) ∈ ks; (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)