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Proof step 9 from proof inv-commit (previous step)

adr = adr3, adr0 = adr3, err = ESUCCESS, pstate = unbuffered, remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, ¬ syn, syn0, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, elems nx ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr3, istore2, istore1, zh, ri, fi), inv(gstore2 \ ginval4), inv(gstore1), inv(istore2), inv(istore1), istore1 ⊑ istore2, ¬ dups(nx) ⊦ ⟪if rp ≠ null ∧ zh[rp].dirty then {apersistence_allocate_ind#(adr3, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, true; istore2, pstate; err); if err = ESUCCESS then btree_commit_rec#(rp, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; adr, err, zh, istore2, pstate, syn0); if err = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore2, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; pstate, syn0; err)}}; if err = ESUCCESS then apersistence_commit#(adr, maxino1, syn0; ginval1, adr0, istore2, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate; err); if err = ESUCCESS then adr3 := adr else if syn then {zh[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore2, 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; istore2)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore2, 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(istore2) ∧ inv(istore1) ∧ istore1 ⊑ istore2 ∧ remove-refsize0(istore1) = istore1 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
zh[rp] = mkznode(r, zbrar, boolvar, boolvar0, m), adr = adr3, adr0 = adr3, err = ESUCCESS, pstate = unbuffered, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, ¬ syn, syn0, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr3, istore2, istore1, zh, ri, fi), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval4), istore1 ⊑ istore2 ⊦ ⟪if rp ≠ null ∧ boolvar0 then {apersistence_allocate_ind#(adr3, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, true; istore2, pstate; err); if err = ESUCCESS then btree_commit_rec#(rp, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; adr, err, zh, istore2, pstate, syn0); if err = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore2, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; pstate, syn0; err)}}; if err = ESUCCESS then apersistence_commit#(adr, maxino1, syn0; ginval1, adr0, istore2, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate; err); if err = ESUCCESS then adr3 := adr else if syn then {zh[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore2, 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; istore2)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore2, 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(istore2) ∧ inv(istore1) ∧ istore1 ⊑ istore2 ∧ remove-refsize0(istore1) = istore1 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn0)), dups(nx)

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] → [zh[rp], r, zbrar, boolvar0, boolvar1, m]

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: zh[rp], r, zbrar, boolvar0, boolvar1, m