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Proof step 62 from proof inv-truncate (previous step)

m2 + m1 = ((range(fi1 \ datakeys(key, n0, fi1)) | m) ∪ (as0 | m)).size, gstore2[m] = groupblock(gndx1, lax1, m2 + m1), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore2 =○refsize gstore3, inv(gstore2[m, groupblock(gndx1, lax1, m2)] \ jro), inv(gstore2 \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), @(m, m0, m1) ∈ range(fi1 \ datakeys(key, n0, fi1)) | m, m ∈ gstore2, @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ # as0 = 0, as0 = ∅, m2 = ((range(fi1 \ datakeys(key, n0, fi1)) | m) ∪ ((as0 | m) -- @(m, m0, m1))).size, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 63:
m2 + m1 = ((range(fi1 \ datakeys(key, n0, fi1)) | m) ∪ (as0 | m)).size, gstore2[m] = groupblock(gndx1, lax1, m2 + m1), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore2 =○refsize gstore3, inv(gstore2[m, groupblock(gndx1, lax1, m2)] \ jro), inv(gstore2 \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), @(m, m0, m1) ∈ fi1 \ datakeys(key, n0, fi1), m ∈ gstore2, @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ # as0 = 0, as0 = ∅, m1 = 0, pmaxino = 0, dups(nx)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m = m + n ↔ n = 0; (s)% ⊦ adr ∈ range ri ↔ adr ∈ ri; (s)% ⊦ @(m, m0, m1) ∈ as | m ↔ @(m, m0, m1) ∈ as; (s)%unc: ⊦ as ∪ as0 = as0 ∪ as; from specification set-union[node-store]%una: ⊦ (as ∪ as0) ∪ as1 = as ∪ as0 ∪ as1; from specification set-union[node-store]% ⊦ adr ∈ as → as ∪ (as0 -- adr) = as ∪ as0; (s)