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Proof step 3 from proof refine-add-gnds (previous step)

gstore = gstore0, ax = ax0, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore0) = istore0, maxino ∈ nx0, gstore0[maxino].size + gndlist.flashsize ≤ LEB_SIZE, btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, fi, fi0, ld), inv(gstore0 \ ginval0), inv(gstore2), flushed(gstore0 \ (ginval0 ∪ elems nx0)), gstore2 \ ginval0 lpt= gstore0 \ elems nx0, ri-inj(fi), ri-inj(fi0), btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, ri, fi1, ld0), inv(istore), inv(istore0), flushed(istore0), istore0 ⊑ istore, maxino ∈ gstore0, ¬ gstore0[maxino].failed, ¬ dups(nx0), ¬ maxino ∈ ginval0 ⊦ ⟪btree_add_gnds#(maxino, gndlist, nx0; ax, gstore0; err)⟫ ⟨index+persistence_add_gnds#(maxino, gndlist, nx0; ax0, gstore; err0)⟩ (gstore = gstore0 ∧ btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, fi, fi0, ld) ∧ ax = ax0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
gstore = gstore0, ax = ax0, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore0) = istore0, maxino ∈ nx0, m0 + gndlist.flashsize ≤ LEB_SIZE, btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, fi, fi0, ld), inv(gstore0 \ ginval0), inv(gstore2), flushed(gstore0 \ (ginval0 ∪ elems nx0)), gstore2 \ ginval0 lpt= gstore0 \ elems nx0, ri-inj(fi), ri-inj(fi0), btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, ri, fi1, ld0), inv(istore), inv(istore0), flushed(istore0), istore0 ⊑ istore, maxino ∈ gstore0, ¬ boolvar, ¬ dups(nx0), ¬ maxino ∈ ginval0, gstore0[maxino] = groupblock(gndlist0, lax, m, m0, m1, boolvar) ⊦ ⟪btree_add_gnds#(maxino, gndlist, nx0; ax, gstore0; err)⟫ ⟨index+persistence_add_gnds#(maxino, gndlist, nx0; ax0, gstore; err0)⟩ (gstore = gstore0 ∧ btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, fi, fi0, ld) ∧ ax = ax0 ∧ err = err0)

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ ( ( ( (gndlist = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.flushindex) ∧ m0 = gblock.size) ∧ m1 = gblock.ref-size) ∧ (boolvar ↔ gblock.failed) ↔ gblock = groupblock(gndlist, lax, m, m0, m1, boolvar) subst: [gblock, gndlist, lax, m, m0, m1, boolvar] → [gstore0[maxino], gndlist0, lax, m, m0, m1, boolvar]

Additional information

Used simplifier rules: ⊦ ( ( ( (gndlist = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.flushindex) ∧ m0 = gblock.size) ∧ m1 = gblock.ref-size) ∧ (boolvar ↔ gblock.failed) ↔ gblock = groupblock(gndlist, lax, m, m0, m1, boolvar); (elim) Used terms: gstore0[maxino], gndlist0, lax, m, m0, m1, boolvar