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Proof step 62 from proof refine-commit (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro3 = ∅, dom remove-refsize0(gstore2) ∩ jro3 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro3, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore1), inv(gstore2 \ jro3), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro3)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-cons(ri, nodes(gstore2 ↓, jro3)), ri-inj(fi1), ri-inj(ri), @(m, m0, m1) ∈ refsize0-addresses((gstore2 \ jro3)↓), @(m, m0, m1) ∈ ri, m ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro3), jvalid2 → jvalid0 ⊦ # refsize0-addresses((gstore2 \ jro3)↓) = 0, #(refsize0-addresses((gstore2 \ jro3)↓) ∩ range ri) = 0, jmaxino = 0, pmaxino = 0, refsize0-addresses((gstore2 \ jro3)↓) = ∅, dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ adr ∈ refsize0-addresses(gstore) ↔ ¬ ¬(adr ∈ gstore ∧ gstore[adr.lnum].ref-size = 0)
Proof step 64:
(gstore2 \ jro3)↓[@(m, m0, m1).lnum].ref-size = 0, remove-refsize0(gstore1) = gstore1, dom remove-refsize0(gstore2) ∩ jro3 = ∅, elems nx ∩ jro3 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro3, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro3), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro3)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro3)), ri-inj(ri), ri-inj(fi1), m ∈ gstore2, @(m, m0, m1) ∈ ri, @(m, m0, m1) ∈ (gstore2 \ jro3)↓, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro3) ⊦ #(refsize0-addresses((gstore2 \ jro3)↓) ∩ range ri) = 0, # refsize0-addresses((gstore2 \ jro3)↓) = 0, jmaxino = 0, pmaxino = 0, refsize0-addresses((gstore2 \ jro3)↓) = ∅, dups(nx)

Rule argument

spec: gjournal-abs name: refsize0-addresses seq: ⊦ adr ∈ refsize0-addresses(gstore) ↔ ¬ ¬(adr ∈ gstore ∧ gstore[adr.lnum].ref-size = 0) subst: [gstore, adr] → [(gstore2 \ jro3)↓, @(m, m0, m1)] flags: <all paths>

Additional information

Used terms: (gstore2 \ jro3)↓, @(m, m0, m1)