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Proof step 548 from proof inv-truncate (previous step)

fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fs[ri[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-closed(ri, fs, ro), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, m2 ≤ n, fo ⊆ dom fi, ro ⊆ dom ri ⊦ m2 % VFS_PAGE_SIZE = 0, fs[ri[inodekey(m)]].directory, buf-opt.some?, dups(log), node-cons ((fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key, fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)), inodekey(0) ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 549:
⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]))
Proof step 550:
fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fs[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-closed(ri, fs, ro), ri-inj(ri), ri-inj(fi), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs, m2 ≤ n, ro ⊆ dom ri, fo ⊆ dom fi, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ m2 % VFS_PAGE_SIZE = 0, fs[ri[inodekey(m)]].directory, buf-opt.some?, dups(log), node-cons ((fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key, fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)), inodekey(0) ∈ ri

Rule argument

spec: aubifs-inv name: ri-cons seq: ⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]])) subst: [fs, ri] → [fs, ri] flags: <all paths>

Additional information

Used terms: fs, ri