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Proof step 8 from proof refine-store (previous step)

gstore ↓[adr] = mkgnode(nd, m, boolvar, boolvar0), remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, p_os.keys.inodes?, jro.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv(gstore0), inv(gstore \ jro0), key-cons(key, nd), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-inj(fi1), ri-inj(ri), adr ∈ nodes(gstore ↓, jro0), adr ∈ gstore, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid → jvalid0 ⊦ jmaxino = 0, pmaxino = 0, dups(nx), key-cons(key, gstore[adr].nd), adr ∈ ri

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: groupnode name: elim seq: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0) subst: [gnd, nd, m, boolvar, boolvar0] → [gstore[adr], nd0, m0, boolvar4, boolvar5]

Additional information

Used simplifier rules: ⊦ adr ∈ nodes(gstore ↓, ginval) ∧ gstore[adr] = gnd → gstore ↓[adr] = gstore[adr]; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)%⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0); (elim) Used terms: gstore[adr], nd0, m0, boolvar4, boolvar5