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

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

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
syn ↔ true, adr = adr1, adr0 = adr2, ginval = ginval2, ginval0 = ginval4, ginval1 = ginval3, gstore = gstore1, gstore0 = gstore2, istore = istore1, istore0 = istore2, maxino = maxino1, maxino0 = maxino2, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval4), istore1 ⊑ istore2, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2 ⊦ ⟪if syn ∧ dom remove-refsize0(gstore0) ∩ ginval0 = ∅ then {fail_or_success#(; ; err); if err = ESUCCESS then {istore0 := remove-refsize0(istore0); istore := istore0; gstore0 := remove-refsize0(gstore0); gstore := gstore0; ginval0 := ∅; adr := adr0; ginval := ginval1; nx := []; maxino := maxino0; pstate := unbuffered} else pstate := readonly; ginval1 := ?} else abort⟫ ( 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)), dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: commit: ⊦ ;