[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 37 from proof inv-lookup (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-cons(fi2, nodes(gstore2 ↓, jro)), ri-inj(fi2), ri-inj(fi1), key ∈ fi2, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ pmaxino = 0, dups(nx), fi2[key] ∈ gstore2 ∧ ¬ fi2[key].lnum ∈ jro

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [fi2[key], m, m0, m1]

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ ri[key] = @(m0, m1, m2) ∧ ri-cons(ri, nodes(gstore ↓, ginval)) → (m0 ∈ ginval ↔ false); (as)%lebs-in-ri-in-gstore-explicit: ⊦ key ∈ ri ∧ ri[key] = adr ∧ ri.lebs ⊆ dom gstore → adr.lnum ∈ gstore; (forward) from specification gjournal-base% ⊦ @(m, m0, m1).lnum = m; (s)%⊦ key ∈ ri ∧ ri[key] = adr ∧ ri-cons(ri, nodes(gstore ↓, ginval)) → adr ∈ gstore; (ss)% ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: fi2[key], m, m0, m1