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Proof step 7 from proof val-trans-01 (previous step)

pos(char2, sortedchars) < pos(char3, sortedchars), pos(char, sortedchars) < pos(char2, sortedchars) ⊦ char < char3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
pos(char, sortedchars) < pos(char3, sortedchars), pos(char2, sortedchars) < pos(char3, sortedchars), pos(char, sortedchars) < pos(char2, sortedchars), pos(char, sortedchars) + 1 < pos(char3, sortedchars) ⊦ char < char3

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%trans-01: ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic