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Proof step 6 from proof abs-dirs-trunc (previous step)

fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri ⊦ mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)) = mkdir (fs[adr, truncnode(key, n)][ri[inodekey(ino)]].size, fs[adr, truncnode(key, n)][ri[inodekey(ino)]].meta, fs[adr, truncnode(key, n)][ri[inodekey(ino)]].nlink, fs[adr, truncnode(key, n)][ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs[adr, truncnode(key, n)], ri)), adr ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri ⊦ adr ∈ ri, fs[ri[inodekey(ino)]].meta = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].meta ∧ fs[ri[inodekey(ino)]].size = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].size ∧ fs[ri[inodekey(ino)]].nlink = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].nlink ∧ fs[ri[inodekey(ino)]].nsubdirs = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].nsubdirs ∧ abs-children(ino, fs, ri) = abs-children(ino, fs[adr, truncnode(key, n)], ri)

Rule argument

Additional information

Used simplifier rules: D-inj: ⊦ mkdir(n0, md0, m0, m1, entries0) = mkdir(n1, md1, m2, m3, entries1) ↔ ¬(md0 ≠ md1 ∨ n0 ≠ n1 ∨ m0 ≠ m2 ∨ m1 ≠ m3 ∨ entries0 ≠ entries1);