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Proof step 34 from proof nodes-transaction (previous step)

# lax = # gndx, # ndx = # gndx1, # lax2 + # lax0 + 1 = # gndx1, gndx1[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), gndx1.last.end, gndx1.head.start, n ∈ gstore, ∀ n. n < # gndx1 → gndx1[n].nd = ndx[n], ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx1 → ¬ gndx1[n0].start) ∧ (n0 + 1 < # gndx1 → ¬ gndx1[n0].end) ⊦ gndx1 = [], nd = ndx[# lax2], dups(lax + lax2), dups(lax0), dups(lax2 + lax0), dups((lax + lax2) + lax0), dups(lax), dups(lax2), @(m2, m3) ∈ lax0, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax, n ∈ ginval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
# ndx = # gndx1, # lax = # gndx, # lax2 + # lax0 + 1 = # gndx1, gstore[n] = groupblock(gndx, lax, m), gndx1[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), gndx1 = gnd + gndx0, gndx1.last.end, gnd.start, n ∈ gstore, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx1 → ¬ gndx1[n0].start) ∧ (n0 + 1 < # gndx1 → ¬ gndx1[n0].end), ∀ n. n < # gndx1 → gndx1[n].nd = ndx[n] ⊦ gndx1 = [], nd = ndx[# lax2], dups(lax2), dups(lax), dups((lax + lax2) + lax0), dups(lax2 + lax0), dups(lax0), dups(lax + lax2), n ∈ ginval, @(m2, m3) ∈ lax, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax0

Rule argument

spec: list-data, inst: group-store name: elim-list-c seq: gndx ≠ [] ⊦ gnd = gndx.head ∧ gndx0 = gndx.tail ↔ gndx = gnd + gndx0 subst: [gndx, gnd, gndx0] → [gndx1, gnd, gndx0]

Additional information

Used simplifier rules: gndx ≠ [] ⊦ gnd = gndx.head ∧ gndx0 = gndx.tail ↔ gndx = gnd + gndx0; (elim) Used terms: gndx1, gnd, gndx0