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Proof step 34 from proof inv-remove (previous step)

fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + m1), 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(gstore2[m, groupblock(gndx, lax, n0)] \ 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) ⊦ pmaxino = 0, dups(nx), (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2[m, groupblock(gndx, lax, n0)], jro)) ∧ refsize-cons(gstore2[m, groupblock(gndx, lax, n0)], range fi2 -- @(m, m0, m1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ refsize-cons(gstore, as) ∧ @(m, m0, m1) ∈ as ∧ m ∈ gstore ∧ gstore[m] = groupblock(gndx, lax, n0 + m1) → refsize-cons(gstore[m, groupblock(gndx, lax, n0)], as -- @(m, m0, m1))
Proof step 36:
fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + 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[m, groupblock(gndx, lax, n0)] \ jro), inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2 -- key), ri-inj(fi2), key ∈ fi2, @(m, m0, m1) ∈ range fi2, m ∈ gstore2, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ pmaxino = 0, dups(nx), (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2[m, groupblock(gndx, lax, n0)], jro)) ∧ true

Rule argument

spec: ablock-store-refsize-cons, inst: group-store name: refsize-cons-remove-index seq: ⊦ refsize-cons(gstore, as) ∧ @(m, m0, m1) ∈ as ∧ m ∈ gstore ∧ gstore[m] = groupblock(gndx, lax, n0 + m1) → refsize-cons (gstore[m, groupblock(gndx, lax, n0)], as -- @(m, m0, m1)) subst: [m1, m0, as, n0, lax, gndx, m, gstore] → [m1, m0, range fi2, n0, lax, gndx, m, gstore2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ ri[key] = adr → adr ∈ range ri; (ss) Used terms: m1, m0, range fi2, n0, lax, gndx, m, gstore2