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Proof step 3 from proof inv-commit (previous step)

adr0 = adr, pstate = unbuffered, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, syn, dom remove-refsize0(gstore) ∩ ginval = ∅, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, btree-inv(rp, adr, istore, istore0, zh, ri, fi), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), istore0 ⊑ istore, ¬ dups(nx) ⊦ ⟪btree_commit#(maxino, rp; ginval0, adr0, zh, adr, istore, istore0, ginval, gstore, gstore0, nx, maxino0, ginval1, pstate, syn; err)⟫ ( (∃ ri, fi. btree-inv(rp, adr, istore, istore0, zh, ri, fi)) ∧ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0 ∧ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn))

User applied rule call right

And obtained the following new goals

Proof step 4:
syn0 ↔ syn, adr0 = adr, adr1 = adr2, adr2 = adr, ginval = ginval2, ginval0 = ginval4, ginval1 = ginval3, gstore = gstore1, gstore0 = gstore2, istore = istore1, istore0 = istore2, maxino1 = maxino, pstate = unbuffered, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, syn, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr, istore2, istore1, zh, ri, fi), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval4), istore1 ⊑ istore2 ⊦ ⟪if dom remove-refsize0(gstore0) ∩ ginval0 = ∅ ∧ pstate = unbuffered ∧ adr1 = adr0 then {err := ESUCCESS; let adr = adr1, syn = false in {if rp ≠ null ∧ zh[rp].dirty then {apersistence_allocate_ind#(adr0, istore, ginval0, gstore0, gstore, nx, maxino0, ginval, syn0; istore0, pstate; err); if err = ESUCCESS then btree_commit_rec#(rp, adr0, istore, ginval0, gstore0, gstore, nx, maxino0, ginval; adr, err, zh, istore0, pstate, syn0); if err = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore0, istore, ginval0, gstore0, gstore, nx, maxino0, ginval; pstate, syn0; err)}}; if err = ESUCCESS then apersistence_commit# (adr, maxino1, syn0; ginval1, adr0, istore0, istore, ginval0, gstore0, gstore, nx, maxino0, ginval, pstate; err); if err = ESUCCESS then adr1 := adr else if syn then {zh[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore0, istore, ginval0, gstore0, gstore, nx, maxino0, ginval, pstate, syn0; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino - adr.size, adr0, istore, ginval0, gstore0, gstore, nx, maxino0, ginval, pstate, syn0; istore0)}}}} else abort⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore0, istore, zh, ri, fi)) ∧ inv(gstore0 \ ginval0) ∧ inv(gstore) ∧ elems nx ∩ ginval0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore ∪ elems nx = dom gstore0 ∪ ginval0 ∧ remove-refsize0(gstore) = gstore ∧ inv(istore0) ∧ inv(istore) ∧ istore ⊑ istore0 ∧ remove-refsize0(istore) = istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore0) ∧ (pstate.index? → pstate.lnum ∈ istore0) ∧ (pstate = unbuffered → syn0)), dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: commit: ⊦ ;