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Proof step 17 from proof inv-remove (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, pmaxino ≠ 0, fi0.inos < pmaxino, fi.inos < jmaxino, p_os < pmaxino, inv(gstore1), inv(gstore2 \ jro), refsize-cons(gstore1, range fi0), refsize-cons(gstore2, range fi), ri-inj(fi0), ri-inj(fi), ri-inj(fi -- key), key ∈ fi, pmaxino ≤ jmaxino, fi0.lebs ⊆ dom gstore1, fi.lebs ⊆ dom gstore2, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪index_get_gblock_refsize#(fi[key].lnum, fi -- key, fi0, jro, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(fi[key].lnum, n - fi[key].size, fi -- key, fi0, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)⟫ ( (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ (fi -- key).lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range(fi -- key)) ∧ 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 18:
fi[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi), refsize-cons(gstore1, range fi0), ri-inj(fi -- key), ri-inj(fi), ri-inj(fi0), key ∈ fi, pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore2, fi0.lebs ⊆ dom gstore1, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪index_get_gblock_refsize#(m, fi -- key, fi0, jro, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(m, n - m1, fi -- key, fi0, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)⟫ ( (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ (fi -- key).lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range(fi -- key)) ∧ inv(gstore2 \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro), pmaxino = 0, dups(nx)

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [fi[key], m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: fi[key], m, m0, m1