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Proof step 2 from proof fsync-pages-others-unchanged (previous step)

files = files0, pcache0 = pcache ⊦ [cache_fsync-pages#(inode, dirs; err, files, pcache, asynced)] ∀ ino. ino ≠ inode.ino ∧ ino ∈ files0 → ino ∈ files ∧ mkfile(files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
files = files0, inode = mkinode(m, md, boolvar, m0, m1, m2), pcache0 = pcache ⊦ [cache_fsync-pages#(inode, dirs; err, files, pcache, asynced)] ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files ∧ mkfile(files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0))

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [inode, m, md, boolvar, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: inode, m, md, boolvar, m0, m1, m2