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Proof step 3 from proof valid-group-nodes-drop (previous step)

n ≤ valid-group-nodes(prefixn(n, gndx)), n ≤ # prefixn(n, gndx) ⊦ valid-group-nodes(prefixn(n, gndx)) = # prefixn(n, gndx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ prefixn(n, gndx) = (n ≤ # gndx ⊃ firstn(n, gndx);gndx)

Rule argument

spec: list-prefixn, inst: group-store name: prefixn seq: ⊦ prefixn(n, gndx) = (n ≤ # gndx ⊃ firstn(n, gndx);gndx) subst: [gndx, n] → [gndx, n] flags: <all paths>

Additional information

Used simplifier rules: valid-group-nodes-le: ⊦ n ≤ valid-group-nodes(gndx) → n ≤ # gndx;%valid-group-nodes-ls: ⊦ n < valid-group-nodes(gndx) → n < # gndx;% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ # firstn(n, gndx) = n; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ n ≤ # gndx → # firstn(n, gndx) = n; (s)% ⊦ ¬ n < n; (s) Used terms: gndx, n