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Proof step 7 from proof natstring-chars (previous step)

char ∈ n→s(m), ∀ m1, char. m1 < m → char ∈ n→s(m1) → char = '0' ∨ char = '9' ∨ char = '8' ∨ char = '7' ∨ char = '6' ∨ char = '5' ∨ char = '4' ∨ char = '3' ∨ char = '2' ∨ char = '1' ⊦ char = '1', char = '2', char = '3', char = '4', char = '5', char = '6', char = '7', char = '8', char = '9', char = '0'

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 10 ≤ n → n→s(n) = n→s(n / 10) + n→s(n % 10)
Proof step 9:
¬ 10 ≤ m, char ∈ n→s(m), ∀ m1, char. m1 < m → char ∈ n→s(m1) → char = '0' ∨ char = '9' ∨ char = '8' ∨ char = '7' ∨ char = '6' ∨ char = '5' ∨ char = '4' ∨ char = '3' ∨ char = '2' ∨ char = '1' ⊦ char = '1', char = '2', char = '3', char = '4', char = '5', char = '6', char = '7', char = '8', char = '9', char = '0'
Proof step 55:
10 ≤ m, char ∈ n→s(m / 10) + n→s(m % 10), ∀ m1, char. m1 < m → char ∈ n→s(m1) → char = '0' ∨ char = '9' ∨ char = '8' ∨ char = '7' ∨ char = '6' ∨ char = '5' ∨ char = '4' ∨ char = '3' ∨ char = '2' ∨ char = '1' ⊦ char = '1', char = '2', char = '3', char = '4', char = '5', char = '6', char = '7', char = '8', char = '9', char = '0'

Rule argument

spec: string2nat inst: name: n2s-rec seq: ⊦ 10 ≤ n → n→s(n) = n→s(n / 10) + n→s(n % 10) subst: [n] → [m] flags: rewrite

Additional information

Used terms: m