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Proof step 23 from proof inv-remove (previous step)

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(fi2 -- key), ri-inj(fi2), ri-inj(fi1), key ∈ fi2, m ∈ gstore2, 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, gstore2[m].ref-size - m1, fi2 -- key, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)⟫ ( (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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, m2), 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), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), ri-inj(fi2 -- key), m ∈ gstore2, key ∈ fi2, 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)⟫ ( (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)

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore2[m], gndx, lax, m2]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore2[m], gndx, lax, m2