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Proof step 7 from proof to-to-leq-inf (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ≤ # x → x + y to n = x to n
Proof step 9:
m ≤ n0 + 1, ∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ (nf to n0) + nf(n0) ' to m = nf to m, m ≤ #(nf to n0)
Proof step 23:
m ≤ n0 + 1, m ≤ #(nf to n0), ∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ (nf to n0) to m = nf to m

Rule argument

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

Additional information

Used terms: m, nf(n0) ', nf to n0