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Proof step 183 from proof inv-commit-rec-ind (previous step)

zh[r0] = mkznode(r2, zbrar0, false, true, n), zh1[r0] = mkznode(r1, zbrar, false, true, m0), dom nodes(istore1) = dom nodes(istore) ∪ (err = ESUCCESS ⊃ ∅ ++ adr;∅), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore0) = istore0, as1 ∩ as0 = ∅, as ∩ as0 = ∅, elems nx ∩ ginval1 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval1, ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore), as1, alladrs, ok) * P))(zh), ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore2) | as, as, alladrs, ok) * P))(zh1), ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore) | as1, as1, alladrs, ok) * P))(zh), (( btree (rp, r0, (err = ESUCCESS ⊃ adr;adr3), height, err ≠ ESUCCESS, ri, nodes(istore1), (err = ESUCCESS ⊃ as1 ++ adr;as1), (err = ESUCCESS ⊃ (alladrs -- adr3) ++ adr;alladrs), ok) * P) )(zh0), btree-sub-clean(r0, n, zh), inv(istore), inv(gstore2 \ ginval1), inv(gstore1), inv(istore2), inv(istore0), inv(istore1), refsize-cons(istore, as0 ∪ as1), refsize-cons(istore2, as0 ∪ as), refsize-cons(istore1, as0 ∪ (err = ESUCCESS ⊃ as1 ++ adr;as1)), m1 ∈ istore1, m ∈ istore1, r0 ∈ zh, r0 ∈ zh1, m ∈ istore2, m1 ∈ istore, m ∈ istore, r0 ∈ zh0, (err = ESUCCESS ⊃ as1 ++ adr;as1) ⊆ (err = ESUCCESS ⊃ (alladrs -- adr3) ++ adr;alladrs), (err = ESUCCESS ⊃ as1 ++ adr;as1) ⊆ dom nodes(istore1), as1 ∩ dom nodes(istore2) ⊆ dom nodes(istore), as1 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), as0 ⊆ dom nodes(istore), as1 ⊆ dom nodes(istore2), as1 ∩ dom nodes(istore2) ⊆ as, as ⊆ dom nodes(istore2), as ⊆ alladrs, alladrs ⊆ dom nodes(istore2), as0 ⊆ dom nodes(istore2), as1 ∩ dom nodes(istore2) ⊆ alladrs, as1 ⊆ alladrs, istore2 ⊑ istore1, istore2 ⊑ istore, istore0 ⊑ istore2, istore0 ⊑ istore, istore ⊑ istore1, istore0 ⊑ istore1, height = 0 → as = ∅, height = 0 → as1 = ∅, err = ESUCCESS → pstate0.index? ∧ ¬ zh0[r0].dirty, err = ESUCCESS → ¬ adr ∈ istore, err = ESUCCESS → ¬ adr ∈ as1, pstate0 = unbuffered → syn, pstate0.index? → pstate0.lnum ∈ istore1, pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore2, err = ESUCCESS ∨ ⌊err⌋ , ∀ 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))) ⊦ dups(nx), adr3 ∈ as1, adr3 ∈ as, (err = ESUCCESS → ¬ zh0[r0].dirty ∧ pstate0.index?) ∧ (∃ as1, alladrs1. refsize-cons(istore1, as0 ∪ as1) ∧ as1 ∩ dom nodes(istore2) ⊆ as ∧ as1 ∩ as0 = ∅ ∧ alladrs1 ⊆ alladrs ∪ as1 ∧ ((btree(rp, r0, (err = ESUCCESS ⊃ adr;adr3), height, err ≠ ESUCCESS, ri, nodes(istore1) | as1, as1, alladrs1, ok) * P))(zh0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 184:
zh1[r0] = mkznode(r1, zbrar, false, true, m0), zh[r0] = mkznode(r2, zbrar0, false, true, n), zh0[r0] = mkznode(r3, zbrar1, boolvar0, boolvar1, m2), dom nodes(istore1) = dom nodes(istore) ∪ (err = ESUCCESS ⊃ ∅ ++ adr;∅), remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval1 = ∅, as ∩ as0 = ∅, as1 ∩ as0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval1, (( btree (rp, r0, (err = ESUCCESS ⊃ adr;adr3), height, err ≠ ESUCCESS, ri, nodes(istore1), (err = ESUCCESS ⊃ as1 ++ adr;as1), (err = ESUCCESS ⊃ (alladrs -- adr3) ++ adr;alladrs), ok) * P) )(zh0), ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore) | as1, as1, alladrs, ok) * P))(zh), ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore2) | as, as, alladrs, ok) * P))(zh1), ((btree(rp, r0, adr3, height, dirty, ri, nodes(istore), as1, alladrs, ok) * P))(zh), btree-sub-clean(r0, n, zh), inv(istore1), inv(istore0), inv(istore2), inv(gstore1), inv(gstore2 \ ginval1), inv(istore), refsize-cons(istore1, as0 ∪ (err = ESUCCESS ⊃ as1 ++ adr;as1)), refsize-cons(istore2, as0 ∪ as), refsize-cons(istore, as0 ∪ as1), r0 ∈ zh0, m ∈ istore, m1 ∈ istore, m ∈ istore2, r0 ∈ zh1, r0 ∈ zh, m ∈ istore1, m1 ∈ istore1, as1 ⊆ alladrs, as1 ∩ dom nodes(istore2) ⊆ alladrs, as0 ⊆ dom nodes(istore2), alladrs ⊆ dom nodes(istore2), as ⊆ alladrs, as ⊆ dom nodes(istore2), as1 ∩ dom nodes(istore2) ⊆ as, as1 ⊆ dom nodes(istore2), as0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), as1 ⊆ dom nodes(istore), as1 ∩ dom nodes(istore2) ⊆ dom nodes(istore), (err = ESUCCESS ⊃ as1 ++ adr;as1) ⊆ dom nodes(istore1), (err = ESUCCESS ⊃ as1 ++ adr;as1) ⊆ (err = ESUCCESS ⊃ (alladrs -- adr3) ++ adr;alladrs), istore0 ⊑ istore1, istore ⊑ istore1, istore0 ⊑ istore, istore0 ⊑ istore2, istore2 ⊑ istore, istore2 ⊑ istore1, pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore2, pstate0.index? → pstate0.lnum ∈ istore1, pstate0 = unbuffered → syn, err = ESUCCESS → ¬ adr ∈ as1, err = ESUCCESS → ¬ adr ∈ istore, err = ESUCCESS → pstate0.index? ∧ ¬ boolvar1, height = 0 → as1 = ∅, height = 0 → as = ∅, err = ESUCCESS ∨ ⌊err⌋ , ∀ 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))) ⊦ dups(nx), adr3 ∈ as, adr3 ∈ as1, (err = ESUCCESS → ¬ boolvar1 ∧ pstate0.index?) ∧ (∃ as1, alladrs1. refsize-cons(istore1, as0 ∪ as1) ∧ as1 ∩ dom nodes(istore2) ⊆ as ∧ as1 ∩ as0 = ∅ ∧ alladrs1 ⊆ alladrs ∪ as1 ∧ ((btree(rp, r0, (err = ESUCCESS ⊃ adr;adr3), height, err ≠ ESUCCESS, ri, nodes(istore1) | as1, as1, alladrs1, ok) * P))(zh0))

Rule argument

spec: znode name: elim seq: ⊦ ( ( (r = znd.parent ∧ zbrar = znd.zbranches) ∧ (boolvar ↔ znd.leaf)) ∧ (boolvar0 ↔ znd.dirty)) ∧ m = znd.usedsize ↔ znd = mkznode(r, zbrar, boolvar, boolvar0, m) subst: [znd, r, zbrar, boolvar, boolvar0, m] → [zh0[r0], r3, zbrar1, boolvar0, boolvar1, m2]

Additional information

Used simplifier rules: ⊦ ( ( (r = znd.parent ∧ zbrar = znd.zbranches) ∧ (boolvar ↔ znd.leaf)) ∧ (boolvar0 ↔ znd.dirty)) ∧ m = znd.usedsize ↔ znd = mkznode(r, zbrar, boolvar, boolvar0, m); (elim) Used terms: zh0[r0], r3, zbrar1, boolvar0, boolvar1, m2