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Proof step 27 from proof inv-remove (previous step)

syn0 ↔ jvalid0, fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, m2), fi3 = fi2 -- key, fi4 = fi1, ginval1 = jro, ginval2 = p_os, gstore3 = gstore1, maxino1 = m, maxino2 = pmaxino, n0 = m2 - m1, nx0 = nx, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore1), inv(gstore2 \ jro), inv-journal(nx, gstore2, gstore1, jro), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi2), ri-inj(fi2 -- key), ri-inj(fi1), key ∈ fi2, m ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ [index_set_gblock_refsize#(m, m2 - m1, fi2 -- key, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)] ( inv-journal(nx0, gstore2, gstore3, ginval1) → (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ (fi2 -- key).lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi2 -- @(m, m0, m1)) ∧ inv(gstore2 \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro), pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
gstore2[m] = groupblock(gndx, lax, m2), fi2[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, pmaxino ≠ 0, 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-inj(fi1), ri-inj(fi2 -- key), ri-inj(fi2), m ∈ gstore2, key ∈ fi2, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ [index_set_gblock_refsize#(m, m2 - m1, fi2 -- key, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)] ( inv(gstore2 \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro → (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ (fi2 -- key).lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi2 -- @(m, m0, m1)))

Rule argument

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)