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Proof step 13 from proof pop-corr (previous step)

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

User applied rule insert equation

And obtained the following new goals

Proof step 12:
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, n < # x ⊦ ar[(1 + i→n(i0) + n) % i→n(i)] = ar[(i→n((i0 + 1) % i) + n) % i→n(i)], # ar = 0, x = []

Rule argument

[inserteqarg: pos: left 2,F,T,()]

Additional information

[[CONCRETESIMPRULES : ()]]