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Proof step 39 from proof refine-allocate-gnd (previous step)

err = ESUCCESS, err = err0, ginval = ginval3, gstore = gstore3, nx = nx0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore2) = gstore2, elems(nx + n) ∩ (ginval -- n) = ∅, elems nx0 ∩ ginval3 = ∅, dom gstore2 ∪ elems(nx + n) = dom gstore[n, groupblock([], [], 0)] ∪ (ginval -- n), dom gstore2 ∪ elems nx0 = dom gstore3 ∪ ginval3, btree-inv(rp, adr, istore2, istore1, zh, fi, fi0), inv(gstore[n, groupblock([], [], 0)] \ (ginval -- n)), inv(istore1), inv(istore2), inv(gstore2), inv(gstore3 \ ginval3), ri-inj(fi0), ri-inj(fi), istore1 ⊑ istore2, journal(n).journal? → nx + n ≠ [] ∧ journal(n).lnum = (nx + n).last ∧ journal(n).lnum ∈ gstore[n, groupblock([], [], 0)], journal(n).index? → journal(n).lnum ∈ istore2, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore3, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨index_allocate_gnd#(fi, fi0, gstore2, maxino0, ginval2, true; ginval3, gstore3, nx0; err1)⟩ (ginval3 = ginval -- n ∧ gstore3 = gstore[n, groupblock([], [], 0)] ∧ nx0 = nx + n ∧ err = err1), pstate = readonly, dups(nx0), dups(nx + n), n ∈ gstore

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
ginval = ginval3, gstore = gstore3, nx = nx0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore2) = gstore2, elems nx0 ∩ ginval3 = ∅, dom gstore2 ∪ elems nx0 = dom gstore3 ∪ ginval3, pstate ≠ readonly, btree-inv(rp, adr, istore2, istore1, zh, fi, fi0), inv(gstore3[n, groupblock([], [], 0)] \ (ginval3 -- n)), inv(istore1), inv(istore2), inv(gstore2), inv(gstore3 \ ginval3), ri-inj(fi0), ri-inj(fi), istore1 ⊑ istore2, ¬ dups(nx0), ¬ n ∈ nx0, ¬ n ∈ gstore3, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore3 ⊦ ⟨index_allocate_gnd#(fi, fi0, gstore2, maxino0, ginval2, true; ginval3, gstore3, nx0; err1)⟩ (ginval3 = ginval -- n ∧ gstore3 = gstore[n, groupblock([], [], 0)] ∧ nx0 = nx + n ' ∧ ESUCCESS = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ ∅ -- n = ∅; (s)% ⊦ n ∈ gstore[n0, gblock] ↔ n = n0 ∨ n ∈ gstore; (ws)% ⊦ (nx + n ').last = n; (s)% ⊦ journal(m).lnum = m; (s)% ⊦ nx + n ' ≠ []; (s)% ⊦ journal(m).journal?; (s)% ⊦ ¬ journal(m).index?; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ dups(nx + n ') ↔ n ∈ nx ∨ dups(nx); (ws)%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ (ns ++ n) ∩ (ns0 -- n) = (ns ∩ ns0) -- n; (s)% ⊦ (ns ∪ (ns0 -- n)) ++ n = (ns ∪ ns0) ++ n; (s)% ⊦ dom gstore[n, gblock] = dom gstore ++ n; (s)%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ (ns ++ n) ∪ ns0 = (ns ∪ ns0) ++ n; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ elems(nx0 + n ') = elems nx0 ++ n; (s)% ⊦ nx + n = nx + n '; (s)