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Proof step 2 from proof app-04 (previous step)

perm(y, x + y), perm(x + y, y) ⊦ x = []

User applied rule structural induction

And closed the goal!

Rule argument

indvar: x

Additional information

Used simplifier rules: del: ⊦ perm(x, a ' + y) ↔ a ∈ x ∧ perm(x -1l a, y);%perm-l: ⊦ perm(a ' + x, y) ↔ a ∈ y ∧ perm(x, y -1l a);%delapp: ⊦ perm(x + y, y -1l a) ↔ x = [] ∧ ¬ a ∈ y;%list freely generated by [], +;;%c: ⊦ a + x = a ' + x; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list