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Proof step 47 from proof crash-exists-h (previous step)

fid0 ∈ fs ⊕ fs1, ∀ fid0. fid0 ∈ fs1 ↔ fid0 ∈ sdt0.fids ∧ fid0 ∈ fs0, ∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid], ∀ fid. fid ∈ fs ↔ fid ∈ tree.fids ∧ fid ∈ fs0, ∀ fid. fid ∈ fs → fs[fid] = fs0[fid], ∀ str0. str0 ∈ sdt0[str, tree] → (∀ fs0. ∃ fs1. (∀ fid. fid ∈ fs1 ↔ fid ∈ sdt0[str, tree][str0].fids ∧ fid ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])), ∀ sdt1, fs0. # sdt1 < # sdt0[str, tree] → (∀ str. str ∈ sdt1 → (∀ fs0. ∃ fs1. (∀ fid. fid ∈ fs1 ↔ fid ∈ sdt1[str].fids ∧ fid ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid]))) → (∃ fs1. (∀ fid0. fid0 ∈ fs1 ↔ fid0 ∈ sdt1.fids ∧ fid0 ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])) ⊦ (fs ⊕ fs1)[fid0] = fs0[fid0], str ∈ sdt0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: file-data-store name: oplus-l-at-left seq: ⊦ fid ∈ fs → (fs ⊕ fs0)[fid] = fs[fid] subst: [fid, fs0, fs] → [fid0, fs1, fs] flags: <all paths>

Additional information

Used terms: fid0, fs1, fs