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Proof step 10 from proof crash-exists-h (previous step)

fid ∈ fs, fid0 ∈ (∅)[fid, fs[fid]] ⊦ (∅)[fid, fs[fid]][fid0] = fs[fid0], ∃ fs0. (∀ fid0. fid0 ∈ fs0 ↔ fid0 = fid) ∧ (∀ fid. fid ∈ fs0 → fs0[fid] = fs[fid])

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [fs[fid], fid, ∅, fid0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ fid ∈ ∅; (s)% ⊦ fid = fid0 → fs[fid0, f][fid] = f; (s) Used terms: fs[fid], fid, ∅, fid0