[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 118 from proof inv-addn (previous step)

# gndx0 = # lax0, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro1 = ∅, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro0, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro1, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(groupblock(gndx0, lax0, m0)), inv(gstore3 \ jro0), inv(gstore2 \ jro1), inv(gstore1), refsize-cons(gstore3, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, dom gstore2 ⊆ dom gstore3, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, ⌊err0⌋ , jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ nx0 = [], pmaxino = 0, dups(nx0), dups(nx1), abs-log(nx0.butlast, gstore3 ↓) + lax0.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) ∧ nodes(gstore3 ↓[nx0.last, groupblock(gndx0, lax0, m0)], jro0) = nodes(gstore2 ↓, jro1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ n ∈ gstore ∧ gblock.gndlist = gstore[n].gndlist ∧ gblock.ladrlist = gstore[n].ladrlist → nodes(gstore[n, gblock], ginval) = nodes(gstore, ginval)
Proof step 120:
# gndx0 = # lax0, groupblock(gndx0, lax0, m0).gndlist = gstore3 ↓[nx0.last].gndlist, groupblock(gndx0, lax0, m0).ladrlist = gstore3 ↓[nx0.last].ladrlist, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro1 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro1, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro0, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore1), inv(gstore2 \ jro1), inv(gstore3 \ jro0), inv(groupblock(gndx0, lax0, m0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, nx0.last ∈ gstore3 ↓, pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, dom gstore2 ⊆ dom gstore3, ⌊err0⌋ , jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ nx0 = [], pmaxino = 0, dups(nx1), dups(nx0), abs-log(nx0.butlast, gstore3 ↓) + lax0.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) ∧ nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1)

Rule argument

spec: gjournal-abs name: nodes-write-nochange seq: ⊦ n ∈ gstore ∧ gblock.gndlist = gstore[n].gndlist ∧ gblock.ladrlist = gstore[n].ladrlist → nodes(gstore[n, gblock], ginval) = nodes(gstore, ginval) subst: [ginval, gblock, n, gstore] → [jro0, groupblock(gndx0, lax0, m0), nx0.last, gstore3 ↓] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)%⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0); (s)%⊦ valid-journal-head(nx, gstore, ginval) ∧ nx ≠ [] ∧ gstore[nx.last] = groupblock(gndx, lax, lnum) → valid-group-nodes(gndx) = # gndx; (s)% ⊦ prefixn(# gndx, gndx) = gndx; (s)% ⊦ inv(groupblock(gndx, lax, m0)) → prefixn(# gndx, lax) = lax; (s) Used terms: jro0, groupblock(gndx0, lax0, m0), nx0.last, gstore3 ↓