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

syn, inv-journal(nx, gstore, gstore0, ginval), ri-inj(fi0), ri-inj(fi), n ∈ gstore ⊦ ⟪index_deallocate_gnd#(n, fi, fi0, gstore0, nx, maxino, ginval0, syn; ginval, gstore; err)⟫ inv-journal(nx, gstore, gstore0, ginval), n ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(gstore \ ginval), inv(gstore0), ri-inj(fi), ri-inj(fi0), n ∈ gstore, n ∈ gstore0, ¬ dups(nx), ¬ n ∈ nx ⊦ ⟪index_deallocate_gnd#(n, fi, fi0, gstore0, nx, maxino, ginval0, true; ginval, gstore; err)⟫ (inv(gstore \ ginval) ∧ elems nx ∩ ginval = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval)

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-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)