[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 49 from proof inv-remove (previous step)

gndx0.last = mkgnode(nd, m3, boolvar, false), gndx1.last = mkgnode(nd0, m5, boolvar0, boolvar1), gstore2[m, groupblock(gndx, lax, n0)][nx.last] = groupblock(gndx0, lax0, m2), gstore2[m] = groupblock(gndx, lax, n0 + m1), fi2[key] = @(m, m0, m1), gstore2[nx.last] = groupblock(gndx1, lax1, m4), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore1), inv(gstore2 \ jro), inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro), inv(groupblock(gndx1, lax1, m4)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-inj(fi2), ri-inj(fi2 -- key), ri-inj(fi1), m ∈ gstore2, key ∈ fi2, nx.last ∈ gstore2[m, groupblock(gndx, lax, n0)], nx.last ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, gndx1 = [] ∨ boolvar1 ⊦ gndx0 = [], nx = [], pmaxino = 0, dups(nx)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: nx.last = m

Additional information

Used simplifier rules: ⊦ n ≠ n0 → gstore[n0, gblock][n] = gstore[n]; (s)% ⊦ n ≠ n0 → (n ∈ gstore[n0, gblock] ↔ n ∈ gstore); (s)%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ gstore[n, gblock][n] = gblock; (s)% ⊦ n ∈ gstore[n, gblock]; (s)%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) Used formulas: nx.last = m