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Proof step 33 from proof initialization (previous step)

⊦ # fill(mkavolume(m), unmapped) = # abs(fill(mkabstractvolume(m), erased)) ∧ (∀ n. n < # fill(mkavolume(m), unmapped) → fill(mkavolume(m), unmapped)[n] = abs(fill(mkabstractvolume(m), erased))[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
n < m ⊦ unmapped = abs(fill(mkabstractvolume(m), erased))[n]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → fill(mkavolume(n), aleb)[m] = aleb; (s)% ⊦ # mkabstractvolume(n) = n; (s)% ⊦ # fill(evol, leb) = # evol; (s)% ⊦ # abs(evol) = # evol; (s)% ⊦ # mkavolume(n) = n; (s)% ⊦ # fill(avol, aleb) = # avol; (s)