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Proof step 1 from proof delpos-atsizeid (conclusion)

⊦ x -p # x = x

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: x

Additional information

Used simplifier rules: delpos-empty: ⊦ [] -p n = [];%delpos-rec: ⊦ (a ' + x) -p (n + 1) = a + (x -p n);%list freely generated by [], +;;% ⊦ a + x = a ' + x; (s)% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ x + y = x + z ↔ y = z; (s)% ⊦ # [] = 0; (s)