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Proof step 16 from proof inv-commit-rec-ind (previous step)

zh[r0] = mkznode(r1, zbrar, false, true, m0), remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval1 = ∅, as ∩ as0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval1, ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore) | as, as, alladrs, ok) * P))(zh), inv(istore0), inv(istore), inv(gstore1), inv(gstore2 \ ginval1), refsize-cons(istore, as0 ∪ as), m ∈ istore, r0 ∈ zh, as0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), as ⊆ alladrs, as ⊆ dom nodes(istore), istore0 ⊑ istore, height = 0 → as = ∅, ∀ height0, zh, r0, r, zbrar, boolvar, m0, adr0, adr1, istore1, istore, pstate, m, istore0, gstore0, nx, ginval, as, as0, gstore, rp, dirty, ri, alladrs, P, adr, ino, ns, err, bv. height0 < height → zh[r0] = mkznode(r, zbrar, boolvar, true, m0) ∧ adr0 = adr1 ∧ istore1 = istore ∧ pstate = index(m) ∧ remove-refsize0(istore0) = istore0 ∧ remove-refsize0(gstore0) = gstore0 ∧ elems nx ∩ ginval = ∅ ∧ as ∩ as0 = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ ((btree(rp, r0, adr1, height0, dirty, ri, nodes(istore) | as, as, alladrs, ok) * P))(zh) ∧ inv(istore0) ∧ inv(istore) ∧ inv(gstore0) ∧ inv(gstore \ ginval) ∧ refsize-cons(istore, as0 ∪ as) ∧ m ∈ istore ∧ r0 ∈ zh ∧ as0 ⊆ dom nodes(istore) ∧ alladrs ⊆ dom nodes(istore) ∧ as ⊆ alladrs ∧ as ⊆ dom nodes(istore) ∧ istore0 ⊑ istore ∧ ¬ dups(nx) ∧ ¬ adr1 ∈ as ∧ (height0 = 0 → as = ∅) → ⟪btree_commit_rec#(r0, adr, istore0, ginval, gstore, gstore0, nx, ino, ns; adr1, err, zh, istore, pstate, bv)⟫ ( istore1 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → bv) ∧ inv(istore) ∧ istore0 ⊑ istore ∧ r0 ∈ zh ∧ (err = ESUCCESS → ¬ zh[r0].dirty ∧ pstate.index?) ∧ (∃ as1, alladrs1. refsize-cons(istore, as0 ∪ as1) ∧ as1 ∩ dom nodes(istore1) ⊆ as ∧ as1 ∩ as0 = ∅ ∧ alladrs1 ⊆ alladrs ∪ as1 ∧ ((btree(rp, r0, (err = ESUCCESS ⊃ adr1;adr0), height0, err ≠ ESUCCESS, ri, nodes(istore) | as1, as1, alladrs1, ok) * P))(zh))) ⊦ commit-inv (0, index(m), istore, istore0, nx, gstore2, gstore1, ginval1, syn, ESUCCESS, rp, r0, adr3, height, dirty, ri, istore, as, as0, alladrs, P, zh), dups(nx), adr3 ∈ as

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: btree-inv name: commit-inv seq: ⊦ commit-inv (n, pstate, istore1, istore0, nx, gstore, gstore0, ginval, bv, err, rp, r, adr, height, dirty, ri, istore, as, as0, alladrs, P, zh) ↔ (∃ as1. refsize-cons(istore, as0 ∪ as1) ∧ as1 ∩ dom nodes(istore1) ⊆ as ∧ as1 ∩ as0 = ∅ ∧ (( btree (rp, r, adr, height, dirty, ri, nodes(istore) | as1, as1, alladrs, ok) * P) )(zh)) ∧ istore1 ⊑ istore ∧ r ∈ zh ∧ n ≤ zh[r].usedsize ∧ zh[r].dirty ∧ ¬ zh[r].leaf ∧ inv-journal(nx, gstore, gstore0, ginval) ∧ inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, bv) ∧ (err = ESUCCESS → pstate.index? ∧ btree-sub-clean(r, n, zh)) subst: [zh, P, alladrs, as0, as, istore, ri, dirty, height, adr, r, rp, err, bv, ginval, gstore0, gstore, nx, istore0, istore1, pstate, n] → [zh, P, alladrs, as0, as, istore, ri, dirty, height, adr3, r0, rp, ESUCCESS, syn, ginval1, gstore1, gstore2, nx, istore0, istore, index(m), 0] flags: <all paths>

Additional information

Used terms: zh, P, alladrs, as0, as, istore, ri, dirty, height, adr3, r0, rp, ESUCCESS, syn, ginval1, gstore1, gstore2, nx, istore0, istore, index(m), 0