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Proof step 43 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), file-node-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0)), inodekey(0) ∈ ri, key ∈ ri ∧ ¬ key ∈ ro ∧ ¬ key.data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
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), inodekey(ino) ∈ replay-log(log0, fs0, fi0 ⊖ fo0), fo0 ⊆ dom fi0, ro ⊆ dom ri, inodekey(ino) ∈ ri ∧ ¬ fs0[ri[inodekey(ino)]].directory → fs0[ri[inodekey(ino)]].nsubdirs = 0 ⊦ fs0[replay-log(log0, fs0, fi0 ⊖ fo0)[inodekey(ino)]].nsubdirs = 0, fs0[replay-log(log0, fs0, fi0 ⊖ fo0)[inodekey(ino)]].directory, dups(log0), inodekey(0) ∈ ri, key ∈ ri ∧ ¬ key ∈ ro ∧ ¬ key.data?

Rule argument

Additional information

Used simplifier rules: ⊦ file-node-cons(fs, ri) → ( file-node-cons(fs0, ri0) ↔ (∀ ino. ( inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → fs[ri[inodekey(ino)]].nsubdirs = 0) → inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0)); (ss)