[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 60 from proof refine-commit (previous step)

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), adr.lnum ∈ gstore2, adr ∈ ri, adr ∈ refsize0-addresses((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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 61:
adr = @(m, m0, m1), 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), adr ∈ refsize0-addresses((gstore2 \ jro3)↓), adr ∈ 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)

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [adr, m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: adr, m, m0, m1