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Proof step 3 from proof at-write-at (previous step)

# ax = # ndx, adr ∈ ax ⊦ fs[ax, ndx][adr] = ndx[pos(adr, ax)], dups(ax)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
#(adr0 + ax0) = # ndx, adr ∈ adr0 + ax0, ∀ ndx, adr, fs. # ax0 = # ndx ∧ adr ∈ ax0 → fs[ax0, ndx][adr] = ndx[pos(adr, ax0)] ∨ dups(ax0) ⊦ fs[adr0 + ax0, ndx][adr] = ndx[pos(adr, adr0 + ax0)], dups(adr0 + ax0)

Rule argument

indvar: ax

Additional information

Used simplifier rules: address-list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ # ndx = 0 ↔ ndx = []; (s)% ⊦ pos(adr, []) = 0; (s)% ⊦ ¬ adr ∈ []; (s)