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Proof step 19 from proof isprefix-add-prefixn-size (previous step)

(# x1 + n) + m = # x0, # x0 + # z = # x1 + # x2, # x2 < n, ∀ n0. n0 < # x1 + # x2 → (x0 + z)[n0] = (x1 + x2)[n0] ⊦ m = 0, x0 = []

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: rotate, discard

Additional information

Used simplifier rules: ⊦ 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%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ¬ m + n < m; (s)