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Proof step 31 from proof inv-remove (previous step)

jvalid ↔ jvalid0, fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, m2), fi = fi1, fi0 = fi2 -- key, gstore = gstore2, gstore0 = gstore1, lnum = m, n = m2 - m1, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore[lnum, gstore[lnum].ref-size:= n] ∪ jro, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore[lnum, gstore[lnum].ref-size:= n] \ jro), inv(gstore1), inv(gstore2 \ jro), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi2), ri-inj(fi2 -- key), ri-inj(fi1), lnum ∈ gstore, key ∈ fi2, m ∈ gstore2, pmaxino ≤ jmaxino, m2 ≥ m1, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ pmaxino = 0, dups(nx), (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore[lnum, gstore[lnum].ref-size:= n], jro)) ∧ (fi2 -- key).lebs ⊆ dom gstore[lnum, gstore[lnum].ref-size:= n] ∧ refsize-cons(gstore[lnum, gstore[lnum].ref-size:= n], range fi2 -- @(m, m0, m1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, m2), 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, m2 - m1)] \ jro), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi2), ri-inj(fi2 -- key), ri-inj(fi1), key ∈ fi2, m ∈ gstore2, pmaxino ≤ jmaxino, m1 ≤ m2, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ pmaxino = 0, dups(nx), (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2[m, groupblock(gndx, lax, m2 - m1)], jro)) ∧ refsize-cons(gstore2[m, groupblock(gndx, lax, m2 - m1)], range fi2 -- @(m, m0, m1))

Rule argument

Additional information

Used simplifier rules: ⊦ groupblock(gndx, lax, m).ref-size:= m0 = groupblock(gndx, lax, m0); (s)% ⊦ ri.lebs ⊆ ns → (ri -- key).lebs ⊆ ns; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ n ∈ gstore → dom gstore ++ n = dom gstore; (s)% ⊦ dom gstore[n, gblock] = dom gstore ++ n; (s)