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Proof step 4 from proof datsize-write-higher (previous step)

datasize(copy(buf0, 0, buf, m, n), # buf) < datasize(buf, # buf), datasize(copy(buf0, 0, buf, m, n), # buf) < m, n ≤ # buf0, m + n ≤ # buf, datasize(buf, # buf) ≤ m ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ m + n ≤ # buf ∧ n ≤ # buf0 ∧ ¬ m < datasize(buf) ∧ m0 ≤ # buf → ¬ datasize(copy(buf0, 0, buf, m, n), m0) < datasize(buf, m0)
Proof step 6:
⊦ datasize(buf) = datasize(buf, # buf)

Rule argument

spec: <toplevel> name: datsize-write-higher-h seq: ⊦ m + n ≤ # buf ∧ n ≤ # buf0 ∧ ¬ m < datasize(buf) ∧ m0 ≤ # buf → ¬ datasize(copy(buf0, 0, buf, m, n), m0) < datasize(buf, m0) subst: [m0, n, m, buf, buf0] → [# buf, n, m, buf, buf0] flags: <all paths>

Additional information

Used simplifier rules: datasize: ⊦ datasize(buf) = datasize(buf, # buf);% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ m; (s) Used terms: # buf, n, m, buf, buf0