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Proof step 1 from proof key-cons-ext (conclusion)

⊦ key-cons(ndx) ↔ (∀ n. n < # ndx → key-cons(ndx[n].key, ndx[n]))

User applied rule structural induction

And obtained the following new goals

Proof step 2:
key-cons(ndx0) ↔ (∀ n. n < # ndx0 → key-cons(ndx0[n].key, ndx0[n])) ⊦ key-cons(nd + ndx0) ↔ (∀ n. n < #(nd + ndx0) → key-cons((nd + ndx0)[n].key, (nd + ndx0)[n]))

Rule argument

indvar: ndx

Additional information

Used simplifier rules: key-cons-base: ⊦ key-cons([]);%node-list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ ¬ m < 0; (s)