[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 45 from proof inv-gc-copy (previous step)

# ax = # ndx1, abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx1], remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, fi2[ndx1.keys, ax].inos < jmaxino0, fi1.inos < pmaxino, fi2.inos < jmaxino3, p_os < pmaxino, jro2 < jmaxino3, LEB_SIZE < nd.flashsize, n0 < nd.flashsize, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro0), inv(gstore3[nx.last]), key-cons(ndx1), key-cons(nd.key, nd), key-cons(ndx2), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, range fi2[ndx1.keys, ax]), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi2[ndx1.keys, ax]), ri-inj(fi1), ri-inj(fi2), nd.key ∈ fi2, nx.last ∈ gstore3, n0 ≤ LEB_SIZE, pmaxino ≤ jmaxino0, pmaxino ≤ jmaxino3, jmaxino3 ≤ jmaxino0, dom gstore2 ⊆ dom gstore3, range fi2[ndx1.keys, ax] ⊆ dom nodes(gstore3 ↓, jro), fi2[ndx1.keys, ax].lebs ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), ndx2.keys.toSet ⊆ dom fi2, ndx1.keys.toSet ⊆ dom fi2, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid1 → valid-journal-head(nx, gstore3, jro) ⊦ jmaxino3 = 0, nx = [], pmaxino = 0, dups(ndx2.keys), dups(ndx1.keys), dups(ndx1.keys + ndx2.keys), dups(nx1), dups(nx), dups(ax), nd.key ∈ ndx2.keys, nd.key ∈ ndx1.keys, ∃ ax0, ndx, ndx0. ndx1 + nd ' + ndx2 = ndx + ndx0 ∧ new(ax0, nodes(gstore2 ↓, jro0)) ∧ ¬ dups(ax0) ∧ # ax0 = # ndx ∧ fi2[ndx1.keys, ax] = fi2[ndx.keys, ax0] ∧ nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, ndx] ∧ abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax0

User applied rule exists right

And closed the goal!

Rule argument

pos: right 12 terms: ax, ndx1, nd ' + ndx2 abort: F discard: T computed: T

Additional information

Used simplifier rules: a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list] Used terms: ax, ndx1, nd ' + ndx2