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Proof step 49 from proof inv-replay (previous step)

replay-log(log0, fs0, fi0 ⊖ fo0) = ri ⊖ ro, 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), key ∈ ri, fo0 ⊆ dom fi0, ro ⊆ dom ri ⊦ key.data?, dups(log0), inodekey(0) ∈ ri ⊖ ro, inodekey(0) ∈ ri, key ∈ ro, ((key ∈ ri → ri[key] ∈ fs0 ∧ node-closed(fs0[ri[key]], ri, fs0, ro)) → key ∈ ri ⊖ ro → ri[key] ∈ fs0 ∧ node-closed(fs0[ri[key]], ri ⊖ ro, fs0, ∅)) ∧ file-node-cons(fs0, ri ⊖ ro) ∧ orphans-cons(fs0, ri ⊖ ro, ∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
replay-log(log0, fs0, fi0 ⊖ fo0) = ri ⊖ ro, 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), key ∈ ri, ro ⊆ dom ri, fo0 ⊆ dom fi0 ⊦ key.data?, dups(log0), key ∈ ro, inodekey(0) ∈ ri, inodekey(0) ∈ ri ⊖ ro, (ri[key] ∈ fs0 ∧ node-closed(fs0[ri[key]], ri, fs0, ro) → key ∈ ri ⊖ ro → node-closed(fs0[ri[key]], ri ⊖ ro, fs0, ∅)) ∧ file-node-cons(fs0, ri ⊖ ro) ∧ orphans-cons(fs0, ri ⊖ ro, ∅)

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)