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Proof step 49 from proof inv-truncate (previous step)

gstore2[m] = groupblock(gndx, lax, n1 + m1), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore2 =○refsize gstore3, inv(gstore2[m, groupblock(gndx, lax, n1)] \ jro), inv(gstore2 \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), m ∈ gstore2, @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ # as0 = 0, as0 = ∅, pmaxino = 0, dups(nx), refsize-cons(gstore2[m, groupblock(gndx, lax, n1)], range(fi1 \ datakeys(key, n0, fi1)) ∪ (as0 -- @(m, m0, m1)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ refsize-cons(gstore, as) ↔ (∀ n. n ∈ gstore → gstore[n].ref-size = (as | n).size)
Proof step 51:
gstore2[m] = groupblock(gndx, lax, n1 + m1), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, p_os < pmaxino, fi1.inos < jmaxino, fi2.inos < pmaxino, gstore2 =○refsize gstore3, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro), inv(gstore2[m, groupblock(gndx, lax, n1)] \ jro), refsize-cons(gstore3, range fi1), refsize-cons(gstore1, range fi2), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi2), @(m, m0, m1) ∈ as0, m ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, as0.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ # as0 = 0, as0 = ∅, pmaxino = 0, dups(nx), ∀ n. n ∈ gstore2[m, groupblock(gndx, lax, n1)] → gstore2[m, groupblock(gndx, lax, n1)][n].ref-size = ((range(fi1 \ datakeys(key, n0, fi1)) ∪ (as0 -- @(m, m0, m1))) | n).size

Rule argument

spec: ablock-store-refsize-cons, inst: group-store name: refsize-cons-def seq: ⊦ refsize-cons(gstore, as) ↔ (∀ n. n ∈ gstore → gstore[n].ref-size = (as | n).size) subst: [as, gstore] → [range(fi1 \ datakeys(key, n0, fi1)) ∪ (as0 -- @(m, m0, m1)), gstore2[m, groupblock(gndx, lax, n1)]] flags: <all paths>

Additional information

Used terms: range(fi1 \ datakeys(key, n0, fi1)) ∪ (as0 -- @(m, m0, m1)), gstore2[m, groupblock(gndx, lax, n1)]