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Proof step 23 from proof rmpos-get (previous step)

x0 = a + y, m + 1 < # x0, m1 + 1 < # x0, m1 < # x0, m1 ≤ m, ∀ m0, n0. m0 < # x0 ∧ n0 + 1 < # x0 → (x0 -1l m0)[n0] = (n0 < m0 ⊃ x0[n0];y[n0]) ⊦ x0 = [], (x0 -1l m1)[m] = y[m]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
m1 < # y, m < # y, m1 ≤ m, ∀ m0, n. ¬ # y < m0 ∧ n < # y → ((a ' + y) -1l m0)[n] = (n < m0 ⊃ (a ' + y)[n];y[n]) ⊦ ((a ' + y) -1l m1)[m] = y[m], y = []

Rule argument

Additional information

Used simplifier rules: l: ⊦ # x = 0 ↔ x = []; from specification list-data%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%succ: ⊦ m +1 = m + 1; from specification nat-basic2%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%c: ⊦ a + x = a ' + x; from specification list