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Proof step 15 from proof crash-exists-h (previous step)

∀ str. str ∈ sdt → (∀ fs0. ∃ fs1. (∀ fid. fid ∈ fs1 ↔ fid ∈ sdt[str].fids ∧ fid ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])) ⊦ ∃ fs1. (∀ fid0. fid0 ∈ fs1 ↔ fid0 ∈ sdt.fids ∧ fid0 ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])

User applied rule induction

And obtained the following new goals

Proof step 16:
∀ str. str ∈ sdt → (∀ fs0. ∃ fs1. (∀ fid. fid ∈ fs1 ↔ fid ∈ sdt[str].fids ∧ fid ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])), ∀ sdt0, fs0. # sdt0 < # sdt → (∀ str. str ∈ sdt0 → (∀ fs0. ∃ fs1. (∀ fid. fid ∈ fs1 ↔ fid ∈ sdt0[str].fids ∧ fid ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid]))) → (∃ fs1. (∀ fid0. fid0 ∈ fs1 ↔ fid0 ∈ sdt0.fids ∧ fid0 ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])) ⊦ ∃ fs1. (∀ fid0. fid0 ∈ fs1 ↔ fid0 ∈ sdt.fids ∧ fid0 ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])

Rule argument

indvar: # sdt wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # sdt