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Proof step 22 from proof datasize-append-empty-h (previous step)

m0 + 1 = n0 + # buf0, (buf0 + buf1)[m0] = empty, datasize(buf1, n0) = 0, m0 < # buf0 + # buf1, # buf0 ≤ m0 + 1, n0 ≤ # buf1, ∀ 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)

User applied rule all left

And obtained the following new goals

Proof step 23:
m0 + 1 = n0 + # buf0, (buf0 + buf1)[m0] = empty, datasize(buf1, n0) = 0, m0 < # buf0 + # buf1, n0 ≤ # buf1, # buf0 ≤ m0 + 1, 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)

Rule argument

pos: left 7 terms: buf0, buf1 abort: F discard: T computed: T

Additional information

Used terms: buf0, buf1