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Proof step 45 from proof crash-exists-h (previous step)

fid ∈ fs ↔ fid ∈ tree.fids ∧ fid ∈ fs0, fid ∈ fs1 ↔ fid ∈ sdt0.fids ∧ fid ∈ fs0, ∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid], ∀ 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])), fid ∈ fs ∨ fid ∈ fs1, ∀ 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])) ⊦ str ∈ sdt0, (fid ∈ sdt0.fids ∨ fid ∈ tree.fids) ∧ fid ∈ fs0

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 2

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