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Proof step 9 from proof valid-group-nodes-shorter-prefix-right (previous step)

(boolvar0 ⊃ # gndx + 1;valid-group-nodes(gndx)) < valid-group-nodes(prefixn(n, gndx + mkgnode(nd, m, boolvar, boolvar0) ')), (boolvar0 ⊃ # gndx + 1;valid-group-nodes(gndx)) < # prefixn(n, gndx + mkgnode(nd, m, boolvar, boolvar0) '), ∀ n1. valid-group-nodes(gndx) < valid-group-nodes(prefixn(n1, gndx)) ∧ valid-group-nodes(gndx) < # prefixn(n1, gndx) → gndx = [] ∨ n1 = 0 ⊦ n = 0

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 1

Additional information

Used simplifier rules: valid-group-nodes-rec: ⊦ valid-group-nodes(gndx + gnd ') = (gnd.end ⊃ # gndx + 1;valid-group-nodes(gndx));% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)% ⊦ # gnd ' = 0 +1; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ # gndx ⊦ prefixn(n, gndx + gndx0) = prefixn(n, gndx); (s)%n ≤ # gndx ⊦ # prefixn(n, gndx) = n; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ m + n < m; (s)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s)% ⊦ mkgnode(nd, m, boolvar, boolvar0).end ↔ boolvar0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)