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Proof step 30 from proof transaction-prefix-app-nonlast (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], false) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, true), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), n0 ≤ # gndx, n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start, n0 < # gndx → ¬ gndx[n0].end, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ' + ndx1)[n], mkgnode(nd, n, ndx = [], false) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], false) ∈ gndx0, mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], false) ⊦ ndx1 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], false) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, true), gndx[n0] = mkgnode(nd4, m3, boolvar3, boolvar6), n0 ≤ # gndx, n0 < # gndx → ¬ boolvar6, n0 ≠ 0 ∧ n0 < # gndx → ¬ boolvar3, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ' + ndx1)[n], mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], false), mkgnode(nd, n, ndx = [], false) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], false) ∈ gndx0 ⊦ ndx1 = []

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] → [gndx[n0], nd4, m3, boolvar3, boolvar6]

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: gndx[n0], nd4, m3, boolvar3, boolvar6