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Proof step 4 from proof write-new-app (previous step)

# ax0 = # ndx0, new(ax0, fs0), new(adr + ax, fs0[ax0, ndx0]), ∀ ax0, ndx0, fs0. # ax0 = # ndx0 ∧ new(ax, fs0[ax0, ndx0]) ∧ new(ax0, fs0) → new(ax, fs0) ⊦ new(adr + ax, fs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# ax0 = # ndx0, new(ax0, fs0), new(ax, fs0[ax0, ndx0]), ∀ ax0, ndx0, fs0. # ax0 = # ndx0 ∧ new(ax, fs0[ax0, ndx0]) ∧ new(ax0, fs0) → new(ax, fs0) ⊦ new(ax, fs0), adr ∈ ax0, adr ∈ fs0

Rule argument

Additional information

Used simplifier rules: new-rec: ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs);%in-write: # ax = # ndx ⊦ adr ∈ fs[ax, ndx] ↔ adr ∈ fs ∨ adr ∈ ax;%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ adr + ax = adr ' + ax; (s)