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Proof step 4 from proof datasize-split-empty (previous step)

buf1 = mkempbuf(# buf1) ⊦ datasize(buf0 + buf1, # buf0 + # buf1) = datasize(buf0, # buf0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ m ≤ # buf ∧ m = # buf0 ∧ m0 ≤ # buf1 ∧ buf = buf0 + buf1 ∧ buf1 = mkempbuf(# buf1) → datasize(buf, # buf0 + m0) = datasize(buf0, # buf0)

Rule argument

spec: <toplevel> name: datasize-split-empty-h seq: ⊦ m ≤ # buf ∧ m = # buf0 ∧ m0 ≤ # buf1 ∧ buf = buf0 + buf1 ∧ buf1 = mkempbuf(# buf1) → datasize(buf, # buf0 + m0) = datasize(buf0, # buf0) subst: [m, buf1, m0, buf0, buf] → [# buf0, buf1, # buf1, buf0, buf0 + buf1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s) Used terms: # buf0, buf1, # buf1, buf0, buf0 + buf1