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Proof step 47 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, datanode(datakey(m, pageno), buf).key = datakey(m, pageno), fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), node-cons(datakey(m, pageno), datanode(datakey(m, pageno), buf)), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri ⊦ replay-one(adr1, datanode(datakey(m, pageno), buf), ri ⊖ ro) = ri[datanode(datakey(m, pageno), buf).key, adr1] ⊖ ro, fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
# buf = VFS_PAGE_SIZE, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri ⊦ (¬ inodekey(m) ∈ ro ⊃ (ri ⊖ ro)[datakey(m, pageno), adr1];ri ⊖ ro) = ri[datakey(m, pageno), adr1] ⊖ ro, fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0

Rule argument

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)% ⊦ node-cons(key0, datanode(key1, buf)) ↔ key0.data?; (s)%⊦ inodekey(ino) ∈ ri → (inodekey(ino) ∈ ri ⊖ ro ↔ ¬ inodekey(ino) ∈ ro); (s)% ⊦ datakey(m, m0).ino = m; (s)%⊦ replay-one(adr, datanode(key, buf), ri) = (inodekey(key.ino) ∈ ri ⊃ ri[key, adr];ri); (s)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ datanode(key, buf).key = key; (s)