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Proof step 2 from proof inv-deallocate-gnd (previous step)

syn, inv-index(istore, istore0), inv-journal(nx, gstore, gstore0, ginval), inv-state(pstate, nx, gstore, istore, syn), n ∈ gstore ⊦ ⟪apersistence_deallocate_gnd#(n, adr, istore, istore0, gstore0, nx, maxino, ginval0, pstate, syn; ginval, gstore; err)⟫ (inv-journal(nx, gstore, gstore0, ginval) ∧ inv-state(pstate, nx, gstore, istore, syn)), n ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), n ∈ gstore, n ∈ gstore0, istore0 ⊑ istore, ¬ dups(nx), ¬ n ∈ nx, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ ⟪apersistence_deallocate_gnd#(n, adr, istore, istore0, gstore0, nx, maxino, ginval0, pstate, true; ginval, gstore; err)⟫ ( inv(gstore \ ginval) ∧ elems nx ∩ ginval = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore))

Rule argument

Additional information

Used simplifier rules: fwd-in-gstore0: ⊦ n ∈ gstore ∧ ¬ n ∈ nx ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ gstore0; (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]%⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)