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Proof step 33 from proof inv-remove (previous step)

gstore2[m] = groupblock(gndx, lax, m2), fi2[key] = @(m, m0, m1), m2 = n0 + m1, 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[m, groupblock(gndx, lax, n0)] \ jro), inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-inj(fi1), ri-inj(fi2 -- key), ri-inj(fi2), m ∈ gstore2, key ∈ fi2, m1 ≤ m2, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ pmaxino = 0, dups(nx), (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2[m, groupblock(gndx, lax, n0)], jro)) ∧ refsize-cons(gstore2[m, groupblock(gndx, lax, n0)], range fi2 -- @(m, m0, m1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + m1), 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), 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, 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, n0)], jro)) ∧ refsize-cons(gstore2[m, groupblock(gndx, lax, n0)], range fi2 -- @(m, m0, m1))

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)