[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 5 from proof lebs-size (previous step)

n + m0 + 1 < # avol, ebm-vol-inv(avol), ∀ n, avol. n + m0 < # avol ∧ ebm-vol-inv(avol) → # lebs(avol, n, m0) = m0 * LEB_SIZE ⊦ # lebs(avol, n, m0 + 1) = LEB_SIZE * m0 + LEB_SIZE

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ n + m < # avol → lebs(avol, n, m + 1) = lebs(avol, n, m) + (avol[n + m].mapped? ⊃ avol[n + m].data + mkempbuf(LEB_SIZE - # avol[n + m].data);mkempbuf(LEB_SIZE))
Proof step 7:
n + m0 + 1 < # avol, n + m0 < # avol, ebm-vol-inv(avol), ∀ n, avol. n + m0 < # avol ∧ ebm-vol-inv(avol) → # lebs(avol, n, m0) = m0 * LEB_SIZE ⊦ #(lebs(avol, n, m0) + (avol[n + m0].mapped? ⊃ avol[n + m0].data + mkempbuf(LEB_SIZE - # avol[n + m0].data);mkempbuf(LEB_SIZE))) = LEB_SIZE * m0 + LEB_SIZE

Rule argument

spec: <toplevel> name: lebs-rec seq: ⊦ n + m < # avol → lebs(avol, n, m + 1) = lebs(avol, n, m) + (avol[n + m].mapped? ⊃ avol[n + m].data + mkempbuf(LEB_SIZE - # avol[n + m].data) ;mkempbuf(LEB_SIZE) ) subst: [m, n, avol] → [m0, n, avol] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ m < n → ¬ m + m0 < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m0, n, avol