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Proof step 11 from proof datasize-append-empty-h (previous step)

(buf0 + buf1)[m0] = empty, m0 < # buf0 + # buf1, # buf0 ≤ m0 + 1 → datasize(buf1, m0 + 1 - # buf0) = 0, ∀ buf0, buf1. m0 ≤ # buf0 + # buf1 ∧ (# buf0 ≤ m0 → datasize(buf1, m0 - # buf0) = 0) → datasize(buf0 + buf1, m0) = datasize(buf0, min(m0, # buf0)) ⊦ datasize(buf0 + buf1, m0) = datasize(buf0, (m0 + 1 < # buf0 ⊃ m0 + 1;# buf0))

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 12:
(buf0 + buf1)[m0] = empty, m0 < # buf0 + # buf1, m0 + 1 < # buf0, # buf0 ≤ m0 + 1 → datasize(buf1, m0 + 1 - # buf0) = 0, ∀ buf0, buf1. m0 ≤ # buf0 + # buf1 ∧ (# buf0 ≤ m0 → datasize(buf1, m0 - # buf0) = 0) → datasize(buf0 + buf1, m0) = datasize(buf0, min(m0, # buf0)) ⊦ datasize(buf0 + buf1, m0) = datasize(buf0, m0 + 1)
Proof step 19:
(buf0 + buf1)[m0] = empty, m0 < # buf0 + # buf1, # buf0 ≤ m0 + 1 → datasize(buf1, m0 + 1 - # buf0) = 0, ∀ buf0, buf1. m0 ≤ # buf0 + # buf1 ∧ (# buf0 ≤ m0 → datasize(buf1, m0 - # buf0) = 0) → datasize(buf0 + buf1, m0) = datasize(buf0, min(m0, # buf0)) ⊦ datasize(buf0 + buf1, m0) = datasize(buf0, # buf0), m0 + 1 < # buf0

Rule argument

pos: right 1

Proof step 11 from proof datasize-append-empty-h (previous step)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

Additional information