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Proof step 7 from proof rmpos-get (previous step)

n < # x0, n < m, m ≤ # x0, ∀ n0, m0. n0 + 1 < # x0 ∧ m0 < # x0 → (x0 -p m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.tail[n0]) ⊦ ((a ' + x0) -p m)[n] = (a ' + x0)[n], x0 = []

User applied rule constructor cut

And obtained the following new goals

Proof step 8:
m = m1 +1, n < m, n < # x0, m ≤ # x0, ∀ n0, m0. n0 + 1 < # x0 ∧ m0 < # x0 → (x0 -p m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.tail[n0]) ⊦ ((a ' + x0) -p m)[n] = (a ' + x0)[n], x0 = []

Rule argument

var: m

Additional information

Used simplifier rules: delpos-base: ⊦ (a ' + x) -p 0 = x;%nat freely generated by 0, +1;;%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ 0 ≤ m; (s)% ⊦ ¬ m < 0; (s)