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Proof step 28 from proof pop-corr (previous step)

a ' + x = tolist(mk(ar, i, i0, n→i(# x) + 1), 1 + # x), i0 < n→i(# ar), inv(mk(ar, i, i0, n→i(# x) + 1)), inv(mk(ar, i, (i0 + 1) % i, n→i(# x))), 0 ≤ i0, x ≠ tolist(mk(ar, i, (i0 + 1) % i, n→i(# x)), # x) ∨ a ≠ ar[i→n(i0)] ⊦ # ar = 0

User applied rule case distinction

And obtained the following new goals

Proof step 18:
x ≠ tolist(mk(ar, i, (i0 + 1) % i, n→i(# x)), # x), a ' + x = tolist(mk(ar, i, i0, n→i(# x) + 1), 1 + # x), i0 < n→i(# ar), inv(mk(ar, i, i0, n→i(# x) + 1)), inv(mk(ar, i, (i0 + 1) % i, n→i(# x))), 0 ≤ i0 ⊦ # ar = 0
Proof step 27:
a ≠ ar[i→n(i0)], a ' + x = tolist(mk(ar, i, i0, n→i(# x) + 1), 1 + # x), i0 < n→i(# ar), inv(mk(ar, i, i0, n→i(# x) + 1)), inv(mk(ar, i, (i0 + 1) % i, n→i(# x))), 0 ≤ i0 ⊦ # ar = 0

Rule argument

[CASEDARG : pos: left 6, ()]

Additional information

[[CONCRETESIMPRULES : ()]]