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Proof step 1 from proof delpos-atsizeid (conclusion)

⊦ x -1l # x = x

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: x

Additional information

Used simplifier rules: delpos-empty: ⊦ [] -1l n = [];%delpos-rec: ⊦ (a ' + x) -1l (n + 1) = a + (x -1l n);%list freely generated by [], +;;%c: ⊦ a + x = a ' + x; from specification list%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%size-01: ⊦ # [] = 0; from specification list-data