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Proof step 21 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])), ∀ 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])) ⊦ ∀ str, tree, sdt0. ¬(sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0), ∃ fs1. (∀ fid0. fid0 ∈ fs1 ↔ fid0 ∈ sdt.fids ∧ fid0 ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
∀ 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])) ⊦ str ∈ sdt0, ∃ fs. (∀ fid. fid ∈ fs ↔ fid ∈ sdt0.fids ∪ tree.fids ∧ fid ∈ fs0) ∧ (∀ fid. fid ∈ fs → fs[fid] = fs0[fid])

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ str ∈ sdt → sdt[str, tree].fids = sdt.fids ∪ tree.fids; (s)