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Proof step 17 from proof inv-replay (previous step)

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-cons-strong(fs0, ri ⊖ ro, ∅, fi0, fo0, log0), 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, ri-closed(ri ⊖ ro, fs0, ∅) ∧ file-node-cons(fs0, ri ⊖ ro) ∧ orphans-cons(fs0, ri ⊖ ro, ∅)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) ↔ replay-safe(log, fs, fi ⊖ fo) ∧ replay(log, fs, fi, fo) = ri ⊖ ro
Proof step 19:
replay(log0, fs0, fi0, fo0) = (ri ⊖ ro) ⊖ ∅, 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), fo0 ⊆ dom fi0, ro ⊆ dom ri ⊦ dups(log0), inodekey(0) ∈ ri ⊖ ro, inodekey(0) ∈ ri, ri-closed(ri ⊖ ro, fs0, ∅) ∧ file-node-cons(fs0, ri ⊖ ro) ∧ orphans-cons(fs0, ri ⊖ ro, ∅)

Rule argument

spec: aubifs-replay name: replay-cons-strong seq: ⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) ↔ replay-safe(log, fs, fi ⊖ fo) ∧ replay(log, fs, fi, fo) = ri ⊖ ro subst: [log, fo, fi, ro, ri, fs] → [log0, fo0, fi0, ∅, ri ⊖ ro, fs0] flags: <all paths>

Additional information

Used terms: log0, fo0, fi0, ∅, ri ⊖ ro, fs0