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Proof step 7 from proof inv-commit-rec (previous step)

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 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, btree-inv(r0, adr1, istore, istore0, zh, ri, fi), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), m ∈ istore, r0 ∈ zh, istore0 ⊑ istore, ¬ dups(nx) ⊦ ⟪btree_commit_rec#(r0, adr1, 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 ∧ (err ≠ ESUCCESS → btree-inv(r0, adr0, istore, istore0, zh, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, adr1, istore, istore, zh, ri, ri) ∧ btree-inv (r0, adr0, istore[adr1.lnum, istore[adr1.lnum].ref-size:= (istore[adr1.lnum].ref-size - adr1.size)], istore0, zh[r0, zh[r0].dirty:= true], ri, fi) ∧ ¬ zh[r0].dirty))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ btree-inv(r, adr, istore, istore0, zh, ri, fi) ↔ (∃ height, dirty, as, alladrs. ((btree(null, r, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore, as) ∧ adr ∈ istore ∧ alladrs ⊆ dom nodes(istore)) ∧ (∃ height, dirty, as, alladrs. ((btree(null, null, adr, height, false, fi, nodes(istore0), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore))
Proof step 9:
zh[r0] = mkznode(r, zbrar, boolvar, true, m0), adr0 = adr1, istore1 = istore, pstate = index(m), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), r0 ∈ zh, m ∈ istore, istore0 ⊑ istore, ∃ height, dirty, as, alladrs. ((btree(null, r0, adr1, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore, as) ∧ adr1 ∈ istore ∧ alladrs ⊆ dom nodes(istore), ∃ height, dirty, as, alladrs. ((btree(null, null, adr1, height, false, fi, nodes(istore0), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore) ⊦ ⟪btree_commit_rec#(r0, adr1, 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 ∧ (err ≠ ESUCCESS → btree-inv(r0, adr0, istore, istore0, zh, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, adr1, istore, istore, zh, ri, ri) ∧ btree-inv (r0, adr0, istore[adr1.lnum, istore[adr1.lnum].ref-size:= (istore[adr1.lnum].ref-size - adr1.size)], istore0, zh[r0, zh[r0].dirty:= true], ri, fi) ∧ ¬ zh[r0].dirty)), dups(nx)

Rule argument

spec: btree-inv name: btree-inv seq: ⊦ btree-inv(r, adr, istore, istore0, zh, ri, fi) ↔ (∃ height, dirty, as, alladrs. (( btree (null, r, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true) )(zh) ∧ refsize-cons(istore, as) ∧ adr ∈ istore ∧ alladrs ⊆ dom nodes(istore)) ∧ (∃ height, dirty, as, alladrs. (( btree (null, null, adr, height, false, fi, nodes(istore0), as, alladrs, ok) * true) )(zh) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore)) subst: [fi, ri, zh, istore0, istore, adr, r] → [fi, ri, zh, istore0, istore, adr1, r0] flags: <all paths>

Additional information

Used terms: fi, ri, zh, istore0, istore, adr1, r0