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Proof step 518 from proof inv-truncate (previous step)

fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fs0[ri[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), node-cons ((fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-closed(ri, fs0, ro), ri-inj(fi), ri-inj(ri), ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, m2 ≤ n, fo ⊆ dom fi, ro ⊆ dom ri, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri → ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0 ∧ key-cons(datakey(m, m2 / VFS_PAGE_SIZE), fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]]), ∀ key. key ∈ ri → ri[key] ∈ fs0 ∧ key-cons(key, fs0[ri[key]]) ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, fs0[ri[inodekey(m)]].directory, buf-opt.some?, dups(log0), inodekey(0) ∈ ri, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ ri, (fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key = datakey(m, m2 / VFS_PAGE_SIZE) ∧ (fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 519:
fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].key = datakey(m, m2 / VFS_PAGE_SIZE), fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fs0[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), node-cons ((fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-closed(ri, fs0, ro), ri-inj(ri), ri-inj(fi), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0, m2 ≤ n, ro ⊆ dom ri, fo ⊆ dom fi, ∀ key. key ∈ ri → ri[key] ∈ fs0 ∧ key-cons(key, fs0[ri[key]]) ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, fs0[ri[inodekey(m)]].directory, buf-opt.some?, dups(log0), adr3 ∈ ri, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, inodekey(0) ∈ ri, (fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key = datakey(m, m2 / VFS_PAGE_SIZE) ∧ (fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).data?

Rule argument

Additional information

Used simplifier rules: ⊦ key-cons(datakey(ino, n), nd) ↔ nd.data? ∧ nd.key = datakey(ino, n); (s)