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Proof step 8 from proof inv-add (previous step)

# xs = xs_len, # xs < h, # ys = 0 ∨ # ys = h ⊦ ⟪xs_len := 1 + xs_len⟫ (#(a + xs) < h ∧ #(a + xs) = xs_len ∧ (# ys = 0 ∨ # ys = h)), xs_len + 1 = h

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ # x = 0 ↔ x = []; (s)% ⊦ a + x = a ' + x; (s)% ⊦ #(a ' + x) = (# x)+1; (s)% ⊦ m +1 = m + 1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≠ n → (m < n ↔ ¬ n < m); (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)