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Proof step 72 from proof ubifs-cons-reduce (previous step)

fs0[ri0[key]].key = key, key.data?, ro0.inodes?, fo0.inodes?, log-cons(log0, fs0), log-cons(log1, fs1), node-closed(fs0[ri0[key]], ri0, fs0, ro0), ri-cons(ri1, fs1), key ∈ ri0, key ∈ ri1, ri0[key] ∈ fs0, fo1 ⊆ dom fi1, ro1 ⊆ dom ri1, ro0 ⊆ dom ri0, fo0 ⊆ dom fi0, key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0, key.dentry? → fs0[ri0[key]].dentry?, key.data? → fs0[ri0[key]].data?, ∀ adr. ( adr ∈ log0 → (fs0[adr].inode? → fs0[adr].key.inode? ∧ fs0[adr].key.ino ≠ 0) ∧ (fs0[adr].dentry? → fs0[adr].key.dentry?) ∧ (fs0[adr].data? → fs0[adr].key.data?) ∧ (fs0[adr].trunc? → fs0[adr].key.inode?)) → adr ∈ log1 → adr ∈ fs1 ∧ (fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0) ∧ (fs1[adr].dentry? → fs1[adr].key.dentry?) ∧ (fs1[adr].data? → fs1[adr].key.data?) ∧ (fs1[adr].trunc? → fs1[adr].key.inode?), ∀ key. key ∈ fo1 → key ∈ fi1, ∀ key. key ∈ ro1 → key ∈ ri1 ⊦ dups(log0), node-closed(fs1[ri1[key]], ri1, fs1, ro1), inodekey(0) ∈ ri1, inodekey(0) ∈ ri0, fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
fs0[ri0[datakey(ino, n)]].key = datakey(ino, n), fs0[ri0[datakey(ino, n)]].data?, ro0.inodes?, fo0.inodes?, log-cons(log0, fs0), log-cons(log1, fs1), node-closed(fs0[ri0[datakey(ino, n)]], ri0, fs0, ro0), ri-cons(ri1, fs1), datakey(ino, n) ∈ ri0, datakey(ino, n) ∈ ri1, ri0[datakey(ino, n)] ∈ fs0, fo1 ⊆ dom fi1, ro1 ⊆ dom ri1, ro0 ⊆ dom ri0, fo0 ⊆ dom fi0, ∀ adr. ( adr ∈ log0 → (fs0[adr].inode? → fs0[adr].key.inode? ∧ fs0[adr].key.ino ≠ 0) ∧ (fs0[adr].dentry? → fs0[adr].key.dentry?) ∧ (fs0[adr].data? → fs0[adr].key.data?) ∧ (fs0[adr].trunc? → fs0[adr].key.inode?)) → adr ∈ log1 → adr ∈ fs1 ∧ (fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0) ∧ (fs1[adr].dentry? → fs1[adr].key.dentry?) ∧ (fs1[adr].data? → fs1[adr].key.data?) ∧ (fs1[adr].trunc? → fs1[adr].key.inode?), ∀ key. key ∈ fo1 → key ∈ fi1, ∀ key. key ∈ ro1 → key ∈ ri1 ⊦ dups(log0), node-closed(fs1[ri1[datakey(ino, n)]], ri1, fs1, ro1), inodekey(0) ∈ ri1, inodekey(0) ∈ ri0, inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory ∧ # fs0[ri0[datakey(ino, n)]].data = VFS_PAGE_SIZE

Rule argument

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ ¬ datakey(m, m0).dentry?; (s)% ⊦ ¬ datakey(m, m0).inode?; (s)