| m0 = m + 1, m0 < 7, ∀ m1, char. m1 < ((m0 + 1) + 1) + 1 → true → ¬ char ∈ '0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9') → ¬ char ∈ s→l(n→s(m1)) ⊦ m0 = 0, ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '1', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '2', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '3', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '4', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '5', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '6', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '7', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '8', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '9', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '0' |
m < 6, ∀ m1, char. m1 < (((m + 1) + 1) + 1) + 1 → true → ¬ char ∈ '0' + '1' + '2' + '3' + '4' + '5' + '6' + '7' + ('8' + '9') → ¬ char ∈ s→l(n→s(m1)) ⊦ ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '1', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '2', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '3', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '4', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '5', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '6', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '7', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '8', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '9', ('4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] = '0'
Used simplifier rules: n < n0 ⊦ m + (* n) < (* n0) ↔ m < n0 - n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≠ 0;