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Proof step 5 from proof rangeeq-till-leb5-fwd (previous step)

m < 5, 5 + n ≤ # avol0, 5 + n ≤ # avol1, ∀ n0. n0 < 5 + n → avol1[n0] = avol0[n0] ⊦ avol1[m] = avol0[m]

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: m

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ ¬ m < n → ¬ m + m0 < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m