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Proof step 6 from proof rmpos-get (previous step)

n < m, m ≤ # x0, n < # x0, ∀ m0, n0. m0 < # x0 ∧ n0 + 1 < # x0 → (x0 -1l m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.rest[n0]) ⊦ x0 = [], ((a ' + x0) -1l m)[n] = (a ' + x0)[n], m = 0

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
m = m1 +1, n < m, m ≤ # x0, n < # x0, ∀ m0, n0. m0 < # x0 ∧ n0 + 1 < # x0 → (x0 -1l m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.rest[n0]) ⊦ x0 = [], ((a ' + x0) -1l m)[n] = (a ' + x0)[n], m = 0

Rule argument

var: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;