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Proof step 71 from proof push-corr (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
0 < i, 0 ≤ i1, 0 ≤ (i0 + i1) % i, inv(mk(ar[i→n((i0 + i1) % i), a], i, i0, 1 + i1)), i1 < i, inv(mk(ar, i, i0, i1)), (i0 + i1) % i < n→i(# ar) ⊦ tolist(mk(ar, i, i0, i1), i→n(i1)) + a ' = tolist(mk(ar[i→n((i0 + i1) % i), a], i, i0, 1 + i1), i→n(i1)) + (ar[i→n((i0 + i1) % i), a][(i→n(i0) + i→n(i1)) % i→n(i)]) ', # ar = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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 : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ mk(ar, i, i0, i1) .len:= i4 = mk(ar, i, i0, i4)], [CSIMPSEQ : ⊦ mk(ar, i, i0, i1) .data:= ar0 = mk(ar0, i, i0, i1)])]]