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Proof step 79 from proof push-corr (previous step)

0 ≤ (buf .first + buf .len) % buf .size, (buf .first + buf .len) % buf .size < n→i(# buf .data), 0 < buf .size, 0 ≤ buf .len, inv(buf), buf .len < buf .size ⊦ # buf .data = 0, (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .size = n→i(# (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .data) ∧ (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .size ≠ 0 ∧ 0 ≤ (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .first ∧ (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .first < (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .size ∧ 0 ≤ (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .len ∧ (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .len ≤ (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .size

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
0 ≤ (buf .first + buf .len) % buf .size, (buf .first + buf .len) % buf .size < n→i(# buf .data), 0 < buf .size, 0 ≤ buf .len, inv(buf), buf .len < buf .size ⊦ # buf .data = 0, buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ buf .first ∧ buf .first < buf .size

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ (buf .len:= i1) .len = i1], [CSIMPSEQ : ⊦ (buf .data:= ar) .first = buf .first], [CSIMPSEQ : ⊦ (buf .len:= i1) .first = buf .first], [CSIMPSEQ : ⊦ # (ar[n, a]) = # ar], [CSIMPSEQ : ⊦ (buf .data:= ar) .data = ar], [CSIMPSEQ : ⊦ (buf .len:= i1) .data = buf .data], [CSIMPSEQ : ⊦ (buf .data:= ar) .size = buf .size], [CSIMPSEQ : ⊦ (buf .len:= i1) .size = buf .size])]]