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Proof step 3 from proof inv-store (previous step)

remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(gstore \ ginval), inv(gstore0), key-cons(key, gstore[adr].nd), ri-inj(fi), ri-inj(fi0), adr ∈ gstore, ¬ dups(nx), ¬ adr ∈ fi ⊦ ⟪index_index_store#(key, adr, fi0, ginval, gstore, gstore0, nx, maxino, ginval0, syn; adr0, syn0, fi)⟫ ri-inj(fi)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
gstore[adr] = mkgnode(nd, m, boolvar, boolvar0), remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(gstore0), inv(gstore \ ginval), key-cons(key, nd), ri-inj(fi0), ri-inj(fi), adr ∈ gstore ⊦ ⟪index_index_store#(key, adr, fi0, ginval, gstore, gstore0, nx, maxino, ginval0, syn; adr0, syn0, fi)⟫ ri-inj(fi), dups(nx), adr ∈ fi

Rule argument

spec: groupnode name: elim seq: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0) subst: [gnd, nd, m, boolvar, boolvar0] → [gstore[adr], nd, m, boolvar, boolvar0]

Additional information

Used simplifier rules: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0); (elim) Used terms: gstore[adr], nd, m, boolvar, boolvar0