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Proof step 326 from proof inv-truncate (previous step)

m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), fs0[ri0[inodekey(m0)]] = inodenode(key1, md, false, m, m1, m2), ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, ri0[key0] ∈ fs0, key0 ∈ ri0, m4 ≤ n1, ro ⊆ dom ri0, key0.data? → fs0[ri0[key0]].data? ∧ inodekey(key0.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key0.ino)]].directory ∧ # fs0[ri0[key0]].data = VFS_PAGE_SIZE, key0.dentry? → fs0[ri0[key0]].dentry? ∧ inodekey(key0.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key0]].ino) ∈ ri0 ∧ ¬ inodekey(key0.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key0]].ino) ∈ ro ∧ fs0[ri0[inodekey(key0.ino)]].directory, key0.inode? → fs0[ri0[key0]].inode? ∧ key0.ino ≠ 0, ¬ key0.data? ∨ key0.ino ≠ m0 ∨ ¬ m4 ≤ key0.part * VFS_PAGE_SIZE ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, inodekey(m0) = key0, m0 = 0, buf-opt.some?, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr3 ∈ ri0, ( (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) = adr3 ∨ (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) = adr2 ∨ (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) = adr1 ∨ (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ∈ fs0) ∧ ( adr3 = (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;( adr2 = (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;( adr1 = (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ truncnode(inodekey(m0), m4) ;fs0 [(key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ] ) ) ) .key = key0 ∧ ( key0.inode? → (adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .inode? ∧ key0.ino ≠ 0) ∧ ( key0.dentry? → (adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .dentry? ∧ inodekey(key0.ino) ∈ ri0 ∧ ( (adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .ino = m0 ∨ inodekey ((adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key0.ino) ∈ ro ∧ ¬ inodekey ((adr3 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .ino) ∈ ro ∧ (adr3 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ truncnode(inodekey(m0), m4);fs0[(m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)])]) ) ) .directory) ∧ ( key0.data? → ( adr3 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;( adr2 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;( adr1 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ truncnode(inodekey(m0), m4) ;fs0 [(key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ] ) ) ) .data? ∧ inodekey(key0.ino) ∈ ri0 ∧ ¬ (adr3 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ truncnode(inodekey(m0), m4);fs0[(m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)])]) ) ) .directory ∧ # ( adr3 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;( adr2 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;( adr1 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ⊃ truncnode(inodekey(m0), m4) ;fs0 [(key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0] ;(inodekey(m0) = key0 ⊃ adr2;(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ) ] ) ) ) .data = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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