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Proof step 9 from proof inv-add-gnds (previous step)

pstate = journal(m), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, pstate.journal?, inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), istore0 ⊑ istore, pstate = unbuffered → syn, pstate.index? → m ∈ istore, pstate.journal? → nx ≠ [] ∧ m = nx.last ∧ m ∈ gstore, pstate.journal? ∨ pstate = readonly ⊦ ⟪apersistence_add_gnds#(gndx, adr, istore, istore0, ginval, gstore0, nx, maxino, ginval0; ax, gstore, pstate, syn; err)⟫ ( inv(gstore \ ginval) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn)), dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
pstate = journal(nx.last), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, nx ≠ [], inv(gstore[nx.last]), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), nx.last ∈ gstore, istore0 ⊑ istore, ¬ dups(nx) ⊦ ⟪apersistence_add_gnds#(gndx, adr, istore, istore0, ginval, gstore0, nx, maxino, ginval0; ax, gstore, pstate, syn; err)⟫ ( inv(gstore \ ginval) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ (pstate.journal? → pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn))

Rule argument

Additional information

Used simplifier rules: fwd-inv-loghead: ⊦ nx ≠ [] ∧ inv(gstore \ ginval) ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(gstore[nx.last]); (forward) from specification apersistence-base%fwd-in-gstore-loghead: ⊦ nx ≠ [] ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → nx.last ∈ gstore; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%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]% ⊦ unbuffered ≠ journal(m); (s)% ⊦ ¬ journal(m).index?; (s)% ⊦ journal(m).journal?; (s)