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

gstore = crash(gstore0, gstore1, ginval0, nx), istore = remove-refsize0(crash(istore0, istore1)), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems nx ∩ ginval0 = ∅, dom gstore1 ∪ elems nx = dom gstore0 ∪ ginval0, btree-inv(rp, adr0, istore0, istore1, zh, ri, fi), inv(gstore0 \ ginval0), inv(gstore1), inv(istore0), inv(istore1), istore1 ⊑ istore0, ¬ dups(nx), pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore0, pstate.index? → pstate.lnum ∈ istore0 ⊦ ⟪btree_recover#(; maxino1, nx1, ginval3, adr1, adr0, istore, istore1, ginval0, gstore, gstore1, nx, maxino, ginval1, pstate0, syn0; rp0, err)⟫ ( err = ESUCCESS → syn0 ∧ (∃ ri, fi. btree-inv(rp0, adr0, istore, istore1, zh0, ri, fi)) ∧ inv(gstore \ ginval0) ∧ inv(gstore1) ∧ elems nx ∩ ginval0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore ∪ ginval0 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore) ∧ inv(istore1) ∧ istore1 ⊑ istore ∧ remove-refsize0(istore1) = istore1 ∧ (pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore) ∧ (pstate0.index? → pstate0.lnum ∈ istore))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
syn ↔ syn0, adr = adr2, adr0 = adr1, ginval = ginval2, ginval1 = ginval3, gstore = gstore1, gstore0 = gstore3, gstore3 = crash(gstore2, gstore1, ginval0, nx), istore = istore1, istore0 = istore3, istore3 = remove-refsize0(crash(istore2, istore1)), maxino0 = maxino1, nx0 = nx1, pstate = pstate0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval0, btree-inv(rp, adr2, istore2, istore1, zh, ri, fi), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval0), istore1 ⊑ istore2, pstate1.index? → pstate1.lnum ∈ istore2, pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore2 ⊦ ⟪apersistence_recover#(; adr0, maxino0, nx0, ginval1, adr, nx, maxino, ginval, istore0, istore, ginval0, gstore0, gstore; pstate, syn, err); rp := null⟫ ( err = ESUCCESS → syn ∧ (∃ ri, fi. btree-inv(rp, adr, istore0, istore, zh0, 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)), dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: recover: ⊦ ;