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Proof step 76 from proof inv-truncate (previous step)

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 \ 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), ri-inj(fi1 \ datakeys(key, n0, fi1)), @(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), m ∈ gstore2, m ∈ gstore3

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0)
Proof step 78:
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), refsize-cons(gstore3, range fi1), refsize-cons(gstore1, range fi2), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), ri-inj(fi2), @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro), ∀ n. n ∈ as0.lebs → n ∈ dom gstore3 ⊦ # as0 = 0, as0 = ∅, pmaxino = 0, dups(nx), m ∈ gstore3, m ∈ gstore2

Rule argument

spec: set-basic, inst: nat-set name: Subset seq: ⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0) subst: [ns0, ns] → [dom gstore3, as0.lebs] flags: <all paths>

Additional information

Used terms: dom gstore3, as0.lebs