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Proof step 14 from proof valid-group-nodes-shorter-prefix (previous step)

valid-group-nodes(prefixn(n0, gndx)) < n0, valid-group-nodes(prefixn(n0, gndx)) < valid-group-nodes(prefixn(n, gndx)), valid-group-nodes(prefixn(n0, gndx)) < n, valid-group-nodes(prefixn(n0, gndx)) < # gndx, n ≤ # gndx, n ≤ n0, n0 ≤ # gndx, ∀ n1, n2. valid-group-nodes(prefixn(n1, gndx)) < valid-group-nodes(prefixn(n2, gndx)) ∧ valid-group-nodes(prefixn(n1, gndx)) < # prefixn(n2, gndx) ∧ n2 ≤ n1 → n2 = 0 ⊦ gndx = []

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 8 terms: n0, n

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%n ≤ # gndx ⊦ # prefixn(n, gndx) = n; (s)% ⊦ m < n → n ≠ 0; (s) Used terms: n0, n