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Proof step 9 from proof inject-n2s (previous step)

n→s(m / 10) + n→s(m % 10) = n→s(n / 10) + n→s(n % 10), 10 ≤ m, 10 ≤ n, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ m = n, m = 0, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ # str0 = # str2 → (str + str0 = str1 + str2 ↔ str = str1 ∧ str0 = str2)
Proof step 11:
# n→s(m % 10) = # n→s(n % 10), n→s(m / 10) = n→s(n / 10) ∧ n→s(m % 10) = n→s(n % 10), 10 ≤ m, 10 ≤ n, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ m = n, m = 0, n = 0

Rule argument

spec: string-less inst: name: append-eqlen-01 seq: ⊦ # str0 = # str2 → (str + str0 = str1 + str2 ↔ str = str1 ∧ str0 = str2) subst: [str2, str1, str0, str] → [n→s(n % 10), n→s(n / 10), n→s(m % 10), n→s(m / 10)] flags: rewrite

Additional information

Used simplifier rules: n2s-length-01: ⊦ # n→s(m % 10) = 1; Used terms: n→s(n % 10), n→s(n / 10), n→s(m % 10), n→s(m / 10)