Proof step 5 from proof insorted (previous step)

User applied rule structural induction

And closed the goal!

Rule argument

Additional information

Used simplifier rules: pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-02: str ≠ "", char ≠ str.char1 ⊦ pos((* char), (* str)) = pos(char, str.rstring) + 1;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%pos-str-03: str ≠ "", char = str.char1 ⊦ pos((* char), (* str)) = 0;%char generated by `a`, `b`, `c`, `d`, `e`, `f`, `g`, `h`, `i`, `j`, `k`, `l`, `m`, `n`, `o`, `p`, `q`, `r`, `s`, `t`, `u`, `v`, `w`, `x`, `y`, `z`, `A`, `B`, `C`, `D`, `E`, `F`, `G`, `H`, `I`, `J`, `K`, `L`, `M`, `N`, `O`, `P`, `Q`, `R`, `S`, `T`, `U`, `V`, `W`, `X`, `Y`, `Z`, `!`, `@`, `#`, `$`, `%`, `^`, `&`, `*`, `_`, `-`, `+`, `=`, `~`, `<`, `>`, `?`, `.`, `:`, `/`, `|`, `0`, `1`, `2`, `3`, `4`, `5`, `6`, `7`, `8`, `9`, `(`, `)`, `[`, `]`, ` ` ;;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2