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Proof step 16 from proof n2s-s2n-identity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ s→n(char ') = pos(char, '0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9'))
Proof step 18:
m < 10, ∀ m1. m1 < m → true → s→n(n→s(m1)) = m1 ⊦ pos (('0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m], '0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9')) = m

Rule argument

spec: inst: name: s2n-char seq: ⊦ s→n(char ') = pos (char, '0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9')) subst: [char] → [( '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ' )[m ]] flags: rewrite, current

Additional information

Used terms: ( '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ' )[m ]