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Proof step 16 from proof n2s-chars (previous step)

'1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ' ≠ [] ∧ m0 ≠ 0, m0 < 9, ∀ m1, char. m1 < m0 + 1 → true → ¬ char ∈ '0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9') → ¬ char ∈ s→l(n→s(m1)) ⊦ ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '1', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '2', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '3', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '4', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '5', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '6', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '7', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '8', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '9', ('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ').rest[m0 - 1] = '0'

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
m0 < 9, ∀ m1, char. m1 < m0 + 1 → true → ¬ char ∈ '0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9') → ¬ char ∈ s→l(n→s(m1)) ⊦ m0 = 0, ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '1', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '2', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '3', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '4', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '5', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '6', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '7', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '8', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '9', ('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m0 - 1] = '0'

Rule argument

Additional information

Used simplifier rules: ⊦ char ' + chars ≠ [];% ⊦ (chars + chars0) + chars1 = chars + chars0 + chars1;% ⊦ (char ' + chars).rest = chars;