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Proof step 23 from proof inject-n2s (previous step)

('0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] ' = n→s(n), m < 10, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ m = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ n < 10 → n→s(n) = ('0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9'))[n] + ""
Proof step 25:
¬ n < 10, ('0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] ' = n→s(n), m < 10, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ m = n
Proof step 28:
n < 10, ('0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] ' = ('0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9'))[n] + "", m < 10, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ m = n

Rule argument

spec: string2nat inst: name: n2s-char seq: ⊦ n < 10 → n→s(n) = ( '0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9') )[n ] + "" subst: [n] → [n] flags: rewrite, current

Additional information

Used terms: n