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Proof step 124 from proof inv-store (previous step)

gstore3[m0] = groupblock(gndx, lax, m3), gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore2), inv(gstore3 \ jro0), inv(gstore3[m0, groupblock(gndx, lax, m3 + m2)] \ jro0), key-cons(key, nd), refsize-cons(gstore2, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi1), ri-inj(fi2[key, @(m0, m1, m2)]), ri-inj(fi2), @(m0, m1, m2) ∈ gstore3, m0 ∈ gstore3, pmaxino ≤ jmaxino, pmaxino ≤ max(key.ino + 1, jmaxino), fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ jmaxino = 0, max(key.ino + 1, jmaxino) = 0, pmaxino = 0, dups(nx), key ∈ fi2, @(m0, m1, m2) ∈ fi2, gstore3[m0, groupblock(gndx, lax, m3 + m2)] =○refsize gstore3 ∧ refsize-cons(gstore3[m0, groupblock(gndx, lax, m3 + m2)], range fi2 ++ @(m0, m1, m2)) ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3[m0, groupblock(gndx, lax, m3 + m2)], jro0)) ∧ fi2.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < max(key.ino + 1, jmaxino)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 125:
⊦ gstore =○refsize gstore0 → (gstore[n, gblock] =○refsize gstore0 ↔ n ∈ gstore ∧ gblock.gndlist = gstore[n].gndlist ∧ gblock.ladrlist = gstore[n].ladrlist)
Proof step 126:
gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), gstore3[m0] = groupblock(gndx, lax, m3), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, gstore3 =○refsize gstore3, inv(gstore3[m0, groupblock(gndx, lax, m3 + m2)] \ jro0), inv(gstore3 \ jro0), inv(gstore2), key-cons(key, nd), refsize-cons(gstore3, range fi2), refsize-cons(gstore2, range fi1), ri-inj(fi2), ri-inj(fi2[key, @(m0, m1, m2)]), ri-inj(fi1), m0 ∈ gstore3, @(m0, m1, m2) ∈ gstore3, pmaxino ≤ max(key.ino + 1, jmaxino), pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore3, fi1.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ jmaxino = 0, max(key.ino + 1, jmaxino) = 0, pmaxino = 0, dups(nx), @(m0, m1, m2) ∈ fi2, key ∈ fi2, (m0 ∈ gstore3 ∧ groupblock(gndx, lax, m3 + m2).gndlist = gstore3[m0].gndlist ∧ groupblock(gndx, lax, m3 + m2).ladrlist = gstore3[m0].ladrlist) ∧ refsize-cons(gstore3[m0, groupblock(gndx, lax, m3 + m2)], range fi2 ++ @(m0, m1, m2)) ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3[m0, groupblock(gndx, lax, m3 + m2)], jro0)) ∧ fi2.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < max(key.ino + 1, jmaxino)

Rule argument

spec: ablock-store-inv, inst: group-store name: except-refsizeeq-write-left seq: ⊦ gstore =○refsize gstore0 → ( gstore[n, gblock] =○refsize gstore0 ↔ n ∈ gstore ∧ gblock.gndlist = gstore[n].gndlist ∧ gblock.ladrlist = gstore[n].ladrlist) subst: [gstore0, gblock, n, gstore] → [gstore3, groupblock(gndx, lax, m3 + m2), m0, gstore3] flags: <all paths>

Additional information

Used simplifier rules: ⊦ gstore =○refsize gstore; (s) Used terms: gstore3, groupblock(gndx, lax, m3 + m2), m0, gstore3