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Proof step 25 from proof abs-files-put (previous step)

ino ∈ files, ⌜ino0⌝ ∈ abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)] ⊦ ino0 ∈ files

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ fid ∈ fs[fid0, f] ↔ fid = fid0 ∨ fid ∈ fs
Proof step 27:
⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files

Rule argument

spec: store, inst: file-data-store name: In-insert seq: ⊦ fid ∈ fs[fid0, f] ↔ fid = fid0 ∨ fid ∈ fs subst: [f, fid0, fs, fid] → [mkfile(md, (content.stream to m).buf), ⌜ino⌝ , abs-files(files), ⌜ino0⌝ ] flags: <all paths>

Additional information

Used simplifier rules: abs-files-in: ⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files;% ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s) Used terms: mkfile(md, (content.stream to m).buf), ⌜ino⌝ , abs-files(files), ⌜ino0⌝