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Proof step 113 from proof inv-gc (previous step)

# ax = # referenced-adrs(lax.to-adr(n1), fi2), # lax = # gndx, gstore2[n1] = groupblock(gndx, lax, m), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, jro1 < jmaxino0, inv(gstore1), inv(gstore2 \ jro0), inv(gstore3 \ jro), inv(groupblock(gndx, lax, m)), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, (range fi2 \ (range fi2 | n1)) ∪ ax.toSet), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), n1 ∈ gstore3, n1 ∈ dom gstore3 ∪ jro, n1 ∈ gstore1, @(n1, m1, m2) ∈ (range fi2 \ (range fi2 | n1)) ∪ ax.toSet, n1 ∈ gstore2, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), dom gstore2 ⊆ dom gstore3, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0) ⊦ #((range fi2 \ (range fi2 | n1)) ∪ ax.toSet) = 0, #(dom gstore3 ∪ jro) = 0, jmaxino = 0, jmaxino0 = 0, m = 0, pmaxino = 0, dom gstore3 ∪ jro = ∅, (range fi2 \ (range fi2 | n1)) ∪ ax.toSet = ∅, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), dups(ax), dups(nx1), dups(nx0), n1 ∈ nx1, n1 ∈ nx0, n1 ∈ jro0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 114:
⊦ adr ∈ as ∪ as0 ↔ adr ∈ as ∨ adr ∈ as0
Proof step 115:
# lax = # gndx, # ax = # referenced-adrs(lax.to-adr(n1), fi2), gstore2[n1] = groupblock(gndx, lax, m), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jro1 < jmaxino0, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(groupblock(gndx, lax, m)), inv(gstore3 \ jro), inv(gstore2 \ jro0), inv(gstore1), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, (range fi2 \ (range fi2 | n1)) ∪ ax.toSet), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), ri-inj(fi1), ri-inj(fi2), n1 ∈ gstore2, n1 ∈ gstore1, n1 ∈ dom gstore3 ∪ jro, n1 ∈ gstore3, pmaxino ≤ jmaxino0, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, dom gstore2 ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), @(n1, m1, m2) ∈ range fi2 \ (range fi2 | n1) ∨ @(n1, m1, m2) ∈ ax.toSet ⊦ #(dom gstore3 ∪ jro) = 0, #((range fi2 \ (range fi2 | n1)) ∪ ax.toSet) = 0, jmaxino = 0, jmaxino0 = 0, m = 0, pmaxino = 0, (range fi2 \ (range fi2 | n1)) ∪ ax.toSet = ∅, dom gstore3 ∪ jro = ∅, dups(nx0), dups(nx1), dups(ax), dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), n1 ∈ jro0, n1 ∈ nx0, n1 ∈ nx1

Rule argument

spec: set-union, inst: node-store name: Union seq: ⊦ adr ∈ as ∪ as0 ↔ adr ∈ as ∨ adr ∈ as0 subst: [as0, as, adr] → [ax.toSet, range fi2 \ (range fi2 | n1), @(n1, m1, m2)] flags: <all paths>

Additional information

Used terms: ax.toSet, range fi2 \ (range fi2 | n1), @(n1, m1, m2)