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Proof step 9 from proof refine-allocate-gnd (previous step)

ginval = ginval3, gstore = gstore3, nx = nx0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore2) = gstore2, elems nx0 ∩ ginval3 = ∅, dom gstore2 ∪ elems nx0 = dom gstore3 ∪ ginval3, btree-inv(rp, adr, istore2, istore1, zh, fi, fi0), inv(istore1), inv(istore2), inv(gstore2), inv(gstore3 \ ginval3), ri-inj(fi0), ri-inj(fi), istore1 ⊑ istore2, ¬ dups(nx0), pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore3 ⊦ [apersistence_allocate_gnd#(adr, istore2, istore1, gstore2, maxino0, ginval2, true; ginval, gstore, nx, pstate; err)] ( inv(gstore \ ginval) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore2 ∪ elems nx = dom gstore ∪ ginval ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore2) → ⟨index_allocate_gnd#(fi, fi0, gstore2, maxino0, ginval2, true; ginval3, gstore3, nx0; err0)⟩ (ginval3 = ginval ∧ gstore3 = gstore ∧ nx0 = nx ∧ err = err0))

User applied rule call right

And obtained the following new goals

Proof step 10:
syn ↔ true, ginval = ginval3, ginval0 = ginval2, gstore = gstore3, gstore0 = gstore2, istore = istore1, istore0 = istore2, maxino = maxino0, nx = nx0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore1) = istore1, elems nx0 ∩ ginval3 = ∅, dom gstore2 ∪ elems nx0 = dom gstore3 ∪ ginval3, btree-inv(rp, adr, istore2, istore1, zh, fi, fi0), inv(gstore3 \ ginval3), inv(gstore2), inv(istore2), inv(istore1), ri-inj(fi), ri-inj(fi0), istore1 ⊑ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore3, pstate.index? → pstate.lnum ∈ istore2 ⊦ [if syn then if pstate = readonly then err := EROFS else {fail_or_success#(; ; err); if err = ESUCCESS then choose n with ¬ n ∈ gstore in gstore[n] := groupblock([], [], 0), nx := nx + n, ginval := ginval -- n, pstate := journal(n)} else abort] ( inv(gstore \ ginval) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore2 ∪ elems nx = dom gstore ∪ ginval ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore2) → ⟨index_allocate_gnd#(fi, fi0, gstore2, maxino0, ginval2, true; ginval3, gstore3, nx0; err0)⟩ (ginval3 = ginval ∧ gstore3 = gstore ∧ nx0 = nx ∧ err = err0)), dups(nx0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_allocate_gnd# (ROOTADR, ISTORE, ISTORE0, GSTORE0, MAXINO, OS, PSYNCED ; GINVAL, GSTORE, NL, PSTATE ; ERR ) {if PSYNCED then if PSTATE = readonly then ERR := EROFS else {fail_or_success#(; ; ERR); if ERR = ESUCCESS then choose N with ¬ N ∈ GSTORE in GSTORE[N] := groupblock([], [], 0), NL := NL + N, GINVAL := GINVAL -- N, PSTATE := journal(N)} else abort };