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Proof step 2 from proof putset-same (previous step)

n < # x ⊦ x[n, x[n]] = x, x = []

User applied rule structural induction

And obtained the following new goals

Proof step 3:
0 < # x ⊦ x[0, x[0]] = x, x = []
Proof step 5:
∀ x. n0 < # x → x[n0, x[n0]] = x ∨ x = [], n0 +1 < # x ⊦ x[n0 +1, x[n0 +1]] = x, x = []

Rule argument

indvar: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;