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

zh[rp] = mkznode(r, zbrar, boolvar, true, m), adr = adr3, err1 = ESUCCESS, istore = istore3[n, indexblock([], [], 0)], pstate = index(n), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, syn0, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr3, istore3, istore1, zh, ri, fi), inv(istore3[n, indexblock([], [], 0)]), inv(istore1), inv(istore3), inv(gstore1), inv(gstore2 \ ginval4), rp ∈ zh, istore1 ⊑ istore3[n, indexblock([], [], 0)], istore1 ⊑ istore3, ¬ dups(nx), ¬ n ∈ istore3 ⊦ ⟪btree_commit_rec#(rp, adr3, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; adr, err1, zh, istore, pstate, syn0); syn := false; adr0 := adr3; if err1 = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; pstate, syn0; err1)}; if err1 = ESUCCESS then apersistence_commit#(adr, maxino1, syn0; ginval1, adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate; err1); if err1 = ESUCCESS then adr3 := adr else if syn then {zh[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino - adr.size, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; istore)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore, istore1, zh, ri, fi)) ∧ inv(gstore2 \ ginval4) ∧ inv(gstore1) ∧ elems nx ∩ ginval4 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore) ∧ inv(istore1) ∧ istore1 ⊑ istore ∧ remove-refsize0(istore1) = istore1 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn0))

User applied rule insert program lemma

And obtained the following new goals

Proof step 35:
adr0 = adr1, istore1 = istore, inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), pstate.index?, inv-state(pstate, nx, gstore, istore, bv), btree-inv(r0, adr0, istore, istore0, zh, ri, fi), r0 ∈ zh, zh[r0].dirty ⊦ ⟪btree_commit_rec#(r0, adr0, istore0, ginval, gstore, gstore0, nx, ino, ns; adr1, err, zh, istore, pstate, bv)⟫ ( istore1 ⊑ istore ∧ inv-state(pstate, nx, gstore, istore, bv) ∧ inv-journal(nx, gstore, gstore0, ginval) ∧ inv-index(istore, istore0) ∧ (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))
Proof step 36:
zh[rp] = mkznode(r, zbrar, boolvar, true, m), adr2 = adr3, adr3 = adr, err1 = ESUCCESS, fi0 = fi, ginval0 = ginval4, gstore3 = gstore2, gstore4 = gstore1, ino0 = maxino0, istore = istore3[n, indexblock([], [], 0)], istore = istore, istore2 = istore, istore4 = istore1, ns0 = ginval, nx0 = nx, pstate = index(n), r1 = rp, remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, ri0 = ri, syn0, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, elems nx ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, zh[rp].dirty, pstate.index?, btree-inv(rp, adr3, istore3, istore1, zh, ri, fi), btree-inv(rp, adr3, istore, istore1, zh, ri, fi), inv(gstore2 \ ginval4), inv(gstore1), inv(istore3), inv(istore1), inv(istore3[n, indexblock([], [], 0)]), inv-index(istore, istore1), inv-journal(nx, gstore2, gstore1, ginval4), inv-state(pstate, nx, gstore2, istore, syn0), rp ∈ zh, istore1 ⊑ istore3, istore1 ⊑ istore3[n, indexblock([], [], 0)] ⊦ [btree_commit_rec#(rp, adr3, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; adr, err1, zh, istore, pstate, syn0)] ( istore2 ⊑ istore ∧ inv-state(pstate, nx0, gstore3, istore, syn0) ∧ inv-journal(nx0, gstore3, gstore4, ginval0) ∧ inv-index(istore, istore4) ∧ (err1 ≠ ESUCCESS → btree-inv(r1, adr2, istore, istore4, zh, ri0, fi0)) ∧ ( err1 = ESUCCESS → btree-inv(r1, adr, istore, istore, zh, ri0, ri0) ∧ btree-inv (r1, adr2, istore[adr.lnum, istore[adr.lnum].ref-size:= (istore[adr.lnum].ref-size - adr.size)], istore4, zh[r1, zh[r1].dirty:= true], ri0, fi0) ∧ ¬ zh[r1].dirty) → ⟪syn := false; adr0 := adr3; if err1 = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; pstate, syn0; err1)}; if err1 = ESUCCESS then apersistence_commit# (adr, maxino1, syn0; ginval1, adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate; err1); if err1 = ESUCCESS then adr3 := adr else if syn then {zh[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino - adr.size, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; istore)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore, istore1, zh, ri, fi)) ∧ inv(gstore2 \ ginval4) ∧ inv(gstore1) ∧ elems nx ∩ ginval4 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore) ∧ inv(istore1) ∧ istore1 ⊑ istore ∧ remove-refsize0(istore1) = istore1 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn0))), dups(nx), n ∈ istore3

Rule argument

spec: <toplevel> name: inv-commit-rec seq: adr0 = adr1, istore1 = istore, inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), pstate.index?, inv-state(pstate, nx, gstore, istore, bv), btree-inv(r0, adr0, istore, istore0, zh, ri, fi), r0 ∈ zh, zh[r0].dirty ⊦ ⟪btree_commit_rec# (r0, adr0, istore0, ginval, gstore, gstore0, nx, ino, ns ; adr1, err, zh, istore, pstate, bv)⟫ ( istore1 ⊑ istore ∧ inv-state(pstate, nx, gstore, istore, bv) ∧ inv-journal(nx, gstore, gstore0, ginval) ∧ inv-index(istore, istore0) ∧ ( 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)) subst: [ns, ino, nx, gstore0, gstore, ginval, istore0, adr0, r0, bv, pstate, istore, zh, err, adr1, ri, fi, istore1] → [ginval, maxino0, nx, gstore1, gstore2, ginval4, istore1, adr3, rp, syn0, pstate, istore, zh, err1, adr, ri, fi, istore] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)%⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)% ⊦ istore ⊑ istore0 ∧ ¬ n ∈ istore0 → istore ⊑ istore0[n, iblock]; (ss)% ⊦ index(m).index?; (s)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)% ⊦ ¬ index(m).journal?; (s)% ⊦ index(m).lnum = m; (s)% ⊦ n ∈ istore[n, iblock]; (s)%⊦ ¬ n ∈ istore ∧ inv(istore) ∧ btree-inv(rp, adr, istore, istore0, zh0, ri, fi) → btree-inv (rp, adr, istore[n, indexblock(indx, lax, 0)], istore0, zh0, ri, fi); (ss)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).dirty ↔ boolvar0; (s)