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Proof step 70 from proof ubifs-cons-reduce (previous step)

fs0[ri0[key]].key = key, key.dentry?, 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]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro0 ∧ fs0[ri0[inodekey(key.ino)]].directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 71:
fs0[ri0[dentrykey(ino, str)]].key = dentrykey(ino, str), fs0[ri0[dentrykey(ino, str)]].dentry?, ro0.inodes?, fo0.inodes?, log-cons(log0, fs0), log-cons(log1, fs1), node-closed(fs0[ri0[dentrykey(ino, str)]], ri0, fs0, ro0), ri-cons(ri1, fs1), dentrykey(ino, str) ∈ ri0, dentrykey(ino, str) ∈ ri1, ri0[dentrykey(ino, str)] ∈ 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[dentrykey(ino, str)]], ri1, fs1, ro1), inodekey(0) ∈ ri1, inodekey(0) ∈ ri0, inodekey(ino) ∈ ri0 ∧ inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ri0 ∧ ¬ inodekey(ino) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ro0 ∧ fs0[ri0[inodekey(ino)]].directory

Rule argument

Additional information

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