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Proof step 12 from proof range-eq-append (previous step)

ar0[n0] = ar1[n1], ∀ ar0, n0, ar1, n1, m1. range=(ar0, n0, ar1, n1, m + m1) ↔ range=(ar0, n0, ar1, n1, m) ∧ range=(ar0, n0 + m, ar1, n1 + m, m1) ⊦ range=(ar0, n0 + 1, ar1, n1 + 1, m1 + m) ↔ range=(ar0, n0 + 1, ar1, n1 + 1, m) ∧ range=(ar0, n0 + m + 1, ar1, n1 + m + 1, m1)

User applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: ar0, n0 + 1, ar1, n1 + 1, m1 abort: F discard: T computed: F

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic Used terms: ar0, n0 + 1, ar1, n1 + 1, m1