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Proof step 13 from proof to-to-leq-inf (previous step)

∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ ((nf to n0) + nf(n0) ' to n0) + ((nf to n0) + nf(n0) ')[n0] ' = nf to n0 + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ n ≤ # x → x + y to n = x to n
Proof step 15:
n0 ≤ #(nf to n0), ∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ ((nf to n0) to n0) + ((nf to n0) + nf(n0) ')[n0] ' = nf to n0 + 1

Rule argument

spec: <toplevel> name: append-to-le seq: ⊦ n ≤ # x → x + y to n = x to n subst: [n, y, x] → [n0, nf(n0) ', nf to n0] flags: <all paths>

Additional information

Used simplifier rules: size-inf-to: ⊦ #(nf to n) = n;% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s) Used terms: n0, nf(n0) ', nf to n0