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Proof step 15 from proof rmpos-get (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 16:
m = m1 +1, m < # x0, m ≤ n, n < # x0, ∀ m0, n0. m0 < # x0 ∧ n0 + 1 < # x0 → (x0 -1l m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.rest[n0]) ⊦ ((a ' + x0) -1l m)[n] = x0[n], x0 = []

Rule argument

var: m

Additional information

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