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Proof step 5 from proof valid-group-nodes-shorter-prefix (previous step)

⊦ (∀ n0, gndx, n1. [] = gndx ∧ valid-group-nodes(prefixn(n0, gndx)) < valid-group-nodes(prefixn(n1, gndx)) ∧ valid-group-nodes(prefixn(n0, gndx)) < # prefixn(n1, gndx) ∧ n1 ≤ n0 → gndx = [] ∨ n1 = 0) ∧ (∀ gndx, gnd. (∀ n0, gndx1, n1. gndx = gndx1 ∧ valid-group-nodes(prefixn(n0, gndx1)) < valid-group-nodes(prefixn(n1, gndx1)) ∧ valid-group-nodes(prefixn(n0, gndx1)) < # prefixn(n1, gndx1) ∧ n1 ≤ n0 → gndx1 = [] ∨ n1 = 0) → (∀ n0, gndx1, n1. gndx + gnd = gndx1 ∧ valid-group-nodes(prefixn(n0, gndx1)) < valid-group-nodes(prefixn(n1, gndx1)) ∧ valid-group-nodes(prefixn(n0, gndx1)) < # prefixn(n1, gndx1) ∧ n1 ≤ n0 → gndx1 = [] ∨ n1 = 0))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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