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Proof step 6 from proof s2n-app (previous step)

∀ str0. str0 = "" ∨ s→n(str2 + str0) = s→n(str2) * 10 ^ # str0 + s→n(str0) ⊦ s→n(char0 ') * 10 ^ # str2 * 10 ^ # str0 + s→n(str2 + str0) = (s→n(char0 ') * 10 ^ # str2 + s→n(str2)) * 10 ^ # str0 + s→n(str0), str0 = "", char0 ' + str2 = "", str2 = ""

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 8:
∀ str0. str0 = "" ∨ s→n(str2 + str0) = s→n(str2) * 10 ^ # str0 + s→n(str0) ⊦ s→n(char0 ') * 10 ^ # str2 * 10 ^ # str0 + s→n(str2 + str0) = (10 ^ # str0 * s→n(char0 ') * 10 ^ # str2 + 10 ^ # str0 * s→n(str2)) + s→n(str0), str0 = "", char0 ' + str2 = "", str2 = ""

Rule argument

spec: nat-mult inst: name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [m0, n, m] → [10 ^ # str0, s→n(str2), s→n(char0 ') * 10 ^ # str2] flags: rewrite

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: 10 ^ # str0, s→n(str2), s→n(char0 ') * 10 ^ # str2