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Proof step 1 from proof valid-indices-write (conclusion)

⊦ valid-indices(ar[n, a], nx) ↔ valid-indices(ar, nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ valid-indices(ar, nx) ↔ nx < # ar
Proof step 3:
⊦ nx < # ar → valid-indices(ar, nx)

Rule argument

Additional information

Used simplifier rules: valid-indices: ⊦ valid-indices(ar, nx) ↔ nx < # ar;%valid-indices-simp: ⊦ nx < # ar → valid-indices(ar, nx);% ⊦ # ar[n, a] = # ar; (s)