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Proof step 8 from proof to-to-leq (previous step)

n0 < # x, n0 < # x, m ≤ n0 + 1, m ≤ # x, ∀ m, x. m ≤ n0 ∧ n0 ≤ # x ∧ m ≤ # x → x to n0 to m = x to m ⊦ (x to n0) + x[n0] ' to m = x to m, x = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ n ≤ # x → x + y to n = x to n
Proof step 10:
¬ m ≤ #(x to n0), n0 < # x, n0 < # x, m ≤ n0 + 1, m ≤ # x, ∀ m, x. m ≤ n0 ∧ n0 ≤ # x ∧ m ≤ # x → x to n0 to m = x to m ⊦ (x to n0) + x[n0] ' to m = x to m, x = []
Proof step 24:
m ≤ #(x to n0), n0 < # x, n0 < # x, m ≤ n0 + 1, m ≤ # x, ∀ m, x. m ≤ n0 ∧ n0 ≤ # x ∧ m ≤ # x → x to n0 to m = x to m ⊦ x to n0 to m = x to m, x = []

Rule argument

spec: stream inst: name: append-to-le seq: ⊦ n ≤ # x → x + y to n = x to n subst: [n, y, x] → [m, x[n0] ', x to n0] flags: rewrite, current

Additional information

Used terms: m, x[n0] ', x to n0