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Proof step 33 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), gndx[n0] = mkgnode(nd4, m3, boolvar3, boolvar6), (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 < # mkgnode(nd0, m, true, boolvar0) ', n0 ≤ # gndx, n0 ≠ 0 ∧ n0 < # gndx → ¬ boolvar3, n0 < # gndx → ¬ boolvar6, ∀ 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], false) ' = mkgnode(nd0, m, boolvar, true) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, false), gndx0.last = mkgnode(nd, n, ndx = [], false), (mkgnode(nd0, m, true, true) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), mkgnode(nd0, m, boolvar, true) ∈ gndx, mkgnode(nd, n, ndx = [], false) ∈ gndx0, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ' + ndx1)[n] ⊦ gndx = [], mkgnode(nd, n, ndx = [], false) = mkgnode(nd0, m, boolvar, true), ndx1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ gnd ∈ gndx → gnd ∈ gndx + gndx0; (s)% ⊦ gnd ≠ gnd0 → (gnd ∈ gnd0 ' + gndx ↔ gnd ∈ gndx); (s)%in-14: ⊦ gnd ' + gndx = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]%in-15: ⊦ gndx + gnd ' = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]%inapp-10: ⊦ gnd ' + gndx = gndx0 + gnd0 ' ∧ gnd ≠ gnd0 → gnd ∈ gndx0 ∧ gnd0 ∈ gndx; (forward) from specification list[group-store]%lapp-04: ⊦ gnd ' + gndx = gndx0 + gnd0 ' ∧ gnd ≠ gnd0 → gndx.last = gnd0; (forward) from specification list-last[group-store]%ni: ⊦ gndx + gnd ' = gndx0 + gndx1 ∧ ¬ gnd ∈ gndx1 → gndx1 = []; (forward) from specification list[group-store]%inapp-08: ⊦ gnd ' + gndx = gndx0 + gnd0 ' ∧ gndx0 ≠ [] → gnd ∈ gndx0 ∧ gnd0 ∈ gndx; (forward) from specification list[group-store]% ⊦ gndx ≠ [] → gndx[0] = gndx.head; (s)% ⊦ # ndx = 0 ↔ ndx = []; (s)% ⊦ # [] = 0; (s)% ⊦ gnd ' = gnd0 ' + gndx ↔ gnd = gnd0 ∧ gndx = []; (ws)% ⊦ [] + gndx = gndx; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ 0 ≤ m; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ gnd '[0] = gnd; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ # gnd ' = 0 +1; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ n < # gndx → (gndx + gndx0)[n] = gndx[n]; (s)