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Proof step 4 from proof refine-sync (previous step)

syn ↔ syn0, ginval = ginval2, gstore = gstore2, istore = istore1, istore0 = istore2, maxino = maxino0, nx = nx0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore2) = gstore2, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, btree-inv(rp, adr, istore2, istore1, zh, fi, fi0), inv(istore1), inv(istore2), inv(gstore2), inv(gstore0 \ ginval0), ri-inj(fi0), ri-inj(fi), istore1 ⊑ istore2, pstate = unbuffered → syn0, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore0 ⊦ ⟪apersistence_sync#(adr, istore0, istore, ginval0, gstore0, gstore, nx, maxino, ginval; pstate, syn; err)⟫ ⟨index_sync#(fi, fi0, ginval0, gstore0, gstore2, nx0, maxino0, ginval2; ; syn1, err0)⟩ ((syn1 ↔ syn) ∧ err = err0), dups(nx0)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 5:
syn ↔ syn0, ginval = ginval2, gstore = gstore2, istore = istore1, istore0 = istore2, maxino = maxino0, nx = nx0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore1) = istore1, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, btree-inv(rp, adr, istore2, istore1, zh, fi, fi0), inv(gstore0 \ ginval0), inv(gstore2), inv(istore2), inv(istore1), ri-inj(fi), ri-inj(fi0), istore1 ⊑ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore0, pstate.index? → pstate.lnum ∈ istore2, pstate = unbuffered → syn0 ⊦ ⟪if pstate = readonly then err := EROFS else if pstate = unbuffered then err := ESUCCESS else {fail_or_success#(; ; err); syn := err = ESUCCESS; skip or pstate := readonly}⟫ ⟨index_sync#(fi, fi0, ginval0, gstore0, gstore2, nx0, maxino0, ginval2; ; syn1, err0)⟩ ((syn1 ↔ syn) ∧ err = err0), dups(nx0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_sync# (ROOTADR, ISTORE, ISTORE0, GINVAL, GSTORE, GSTORE0, NL, MAXINO, OS ; PSTATE, PSYNCED ; ERR ) {if PSTATE = readonly then ERR := EROFS else if PSTATE = unbuffered then ERR := ESUCCESS else {fail_or_success#(; ; ERR); PSYNCED := ERR = ESUCCESS; skip or PSTATE := readonly} };