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Proof step 6 from proof datasize-split-empty-h (previous step)

buf1 = mkempbuf(# buf1), m0 ≤ # buf1, # buf0 + m0 ≤ # buf0 + # buf1 ⊦ (# buf0 + m0 ≤ # buf0 ∨ datasize(buf1, # buf0 + m0 - # buf0) = 0 ⊃ datasize(buf0, min(# buf0 + m0, # buf0)) ;# buf0 + datasize(buf1, # buf0 + m0 - # buf0) ) = datasize(buf0, # buf0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
buf1 = mkempbuf(# buf1), m0 ≤ # buf1 ⊦ (m0 = 0 ∨ datasize(buf1, m0) = 0 ⊃ datasize(buf0, # buf0);# buf0 + datasize(buf1, m0)) = datasize(buf0, # buf0)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ min(n0 + m, m) = m; (s)% ⊦ m + n - m = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)