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Proof step 5 from proof at-write-at (previous step)

# ax = # ndx, ∃ ax0, ax1. ax = ax0 + (adr + ax1) ⊦ fs[ax, ndx][adr] = ndx[pos(adr, ax)], dups(ax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# ax1 + # ax0 + 1 = # ndx ⊦ fs[ax1 + adr ' + ax0, ndx][adr] = ndx[# ax1], dups(ax1 + ax0), dups(ax1), dups(ax0), adr ∈ ax1, adr ∈ ax0

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(ax + ax0) → ¬ dups(ax) ∧ ¬ dups(ax0); (forward) from specification list-dup[address-list-set]%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ pos(adr, adr ' + ax) = 0; (s)% ⊦ ¬ adr ∈ ax → pos(adr, ax + ax0) = pos(adr, ax0) + # ax; (s)% ⊦ dups(ax + adr ' + ax0) ↔ adr ∈ ax ∨ adr ∈ ax0 ∨ dups(ax + ax0); (ws)% ⊦ m +1 = m + 1; (s)% ⊦ #(adr ' + ax) = (# ax)+1; (s)% ⊦ #(ax + ax0) = # ax + # ax0; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ adr + ax = adr ' + ax; (s)