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Proof step 22 from proof inv-lookup (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, pmaxino ≠ 0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore1), inv(gstore2 \ jro), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro)), ri-inj(fi1), ri-inj(fi2), key ∈ fi2, fi2[key] ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, ¬ dups(nx), ¬ fi2[key].lnum ∈ jro, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪fail_or_success#(; ; err); if err = ESUCCESS then gnd := gstore2[fi2[key]] else gnd := ?; if err = ESUCCESS then nd := gnd.nd⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
fi2[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-cons(fi2, nodes(gstore2 ↓, jro)), ri-inj(fi2), ri-inj(fi1), fi2[key] ∈ gstore2, key ∈ fi2, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪fail_or_success#(; ; err); if err = ESUCCESS then gnd := gstore2[fi2[key]] else gnd := ?; if err = ESUCCESS then nd := gnd.nd⟫ true, pmaxino = 0, dups(nx), m ∈ jro

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] → [fi2[key], m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: fi2[key], m, m0, m1