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Proof step 31 from proof pop-corr (previous step)

buf = mk(ar, i, i0, i1), i1 = n→i(# x) + 1, a ' + x = tolist(buf, 1 + # x), inv(buf .first:= ((i0 + 1) % i) .len:= n→i(# x)), 0 ≤ i0, i0 < n→i(# ar), inv(buf), ¬ abs(buf .first:= ((i0 + 1) % i) .len:= n→i(# x), x) ∨ a ≠ ar[i→n(i0)] ⊦ # ar = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
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, ¬ abs(mk(ar, i, (i0 + 1) % i, n→i(# x)), x) ∨ a ≠ ar[i→n(i0)] ⊦ # ar = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ a ∈ b ' ↔ a = b], [CSIMPSEQ : ⊦ a ∈ x0 + x1 ↔ ¬ ¬ (a ∈ x0 ∨ a ∈ x1)], [CSIMPSEQ : ⊦ 0 < m ↔ m ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPFORWARD : ⊦ a ' + x0 = x1 → a ∈ x1], [CSIMPSEQ : ⊦ mk(ar, i, i0, i1) .len:= i4 = mk(ar, i, i0, i4)], [CSIMPSEQ : ⊦ mk(ar, i, i0, i1) .first:= i3 = mk(ar, i, i3, i1)])]]