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Proof step 42 from proof truncate-same-iso (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[ino0] = mkfile(m2, md0, # links(ino0, dirs), content0), files0[ino] = mkfile(m, md, # links(ino, dirs), content), afs-cons(dirs, files0), ino ∈ files0, ino0 ∈ files0, m2 / VFS_PAGE_SIZE ∈ content0 ⊦ m2 % VFS_PAGE_SIZE = 0, m = (ino = ino0 ⊃ mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ) .size ∧ md = (ino = ino0 ⊃ mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ) .meta ∧ # links(ino, dirs) = (ino = ino0 ⊃ mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ) .nlink ∧ content.stream to (ino = ino0 ⊃ mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ) .size = (ino = ino0 ⊃ mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ) .content .stream to (ino = ino0 ⊃ mkfile (m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ) .size

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
(ino = ino0 ⊃ mkfile(m2, md0, # links(ino0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ) = mkfile(m0, md1, m1, content1), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[ino] = mkfile(m, md, # links(ino, dirs), content), files0[ino0] = mkfile(m2, md0, # links(ino0, dirs), content0), afs-cons(dirs, files0), m2 / VFS_PAGE_SIZE ∈ content0, ino0 ∈ files0, ino ∈ files0 ⊦ m2 % VFS_PAGE_SIZE = 0, m = m0 ∧ md = md1 ∧ # links(ino, dirs) = m1 ∧ content.stream to m0 = content1.stream to m0

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [(ino = ino0 ⊃ mkfile (m2, md0, # links(ino0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ), m0, md1, m1, content1]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: (ino = ino0 ⊃ mkfile (m2, md0, # links(ino0, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ;mkfile(m, md, # links(ino, dirs), content) ), m0, md1, m1, content1