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Proof step 3 from proof datasize-empbuf (previous step)

⊦ datasize(buf + mkempbuf(n), # buf + n) = datasize(buf, # buf)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ m ≤ # buf + n → datasize(buf + mkempbuf(n), m) = datasize(buf, min(# buf, m))
Proof step 5:
m ≤ # buf0 ⊦ datasize(buf0 + buf1, m) = datasize(buf0, m)

Rule argument

spec: <toplevel> name: datasize-empbuf-h seq: ⊦ m ≤ # buf + n → datasize(buf + mkempbuf(n), m) = datasize(buf, min(# buf, m)) subst: [m, n, buf] → [# buf + n, n, buf] flags: <all paths>

Additional information

Used simplifier rules: datasize-append-lower-h: m ≤ # buf0 ⊦ datasize(buf0 + buf1, m) = datasize(buf0, m);% ⊦ min(n0 + m, m) = m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: # buf + n, n, buf