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Proof step 3 from proof to-plus-from-fin (previous step)

∀ n. n ≤ # x0 → (x0 to n) + (x0 from n) = x0, n ≤ #(a + x0) ⊦ (a + x0 to n) + (a + x0 from n) = a + x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n ≤ # x0 + 1, ∀ n. n ≤ # x0 → (x0 to n) + (x0 from n) = x0 ⊦ (a ' + x0 to n) + (a ' + x0 from n) = a ' + x0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%c: ⊦ a + x = a ' + x; from specification list