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Proof step 24 from proof n2s-s2n-identity (previous step)

m0 < 9, ∀ m1. m1 < m0 + 1 → true → s→n(n→s(m1)) = m1 ⊦ pos (('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = m0 + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
n ≠ 0 ⊦ (char ' + chars)[(* n)] = chars[n -1]
Proof step 26:
¬ m0 ≠ 0, m0 < 9, ∀ m1. m1 < m0 + 1 → true → s→n(n→s(m1)) = m1 ⊦ pos (('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = m0 + 1
Proof step 29:
m0 ≠ 0, m0 < 9, ∀ m1. m1 < m0 + 1 → true → s→n(n→s(m1)) = m1 ⊦ pos (('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 -1], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = m0 + 1

Rule argument

spec: list-del inst: charlist name: get-numrec seq: n ≠ 0 ⊦ (char ' + chars)[(* n)] = chars[n -1] subst: [n, chars, char] → [m0, '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ', '1'] flags: rewrite

Additional information

Used terms: m0, '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ', '1'