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Proof step 37 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), gndx0[m4] = mkgnode(nd3, m2, boolvar5, true), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), gndx[n0] = mkgnode(nd4, m3, boolvar3, boolvar6), n0 = m4 + 1, n0 ≤ # gndx, 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) ⊦ n0 = 0, ndx1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], false) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), gndx0[m4] = mkgnode(nd3, m2, boolvar5, true), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), gndx[m4 + 1] = mkgnode(nd4, m3, boolvar3, boolvar6), m4 < # gndx, mkgnode(nd, n, ndx = [], false) ∈ gndx0, mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx, m4 + 1 < # gndx → ¬ boolvar3, m4 + 1 < # gndx → ¬ boolvar6, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ' + ndx1)[n] ⊦ gndx = [], ndx1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ gnd ' + gndx = gndx0 + gndx1 → (gnd ∈ gndx0 ↔ gndx0 ≠ []); (ss)% ⊦ # ndx = 0 ↔ ndx = []; (s)%ni: ⊦ gndx + gnd ' = gndx0 + gndx1 ∧ ¬ gnd ∈ gndx1 → gndx1 = []; (forward) from specification list[group-store]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%inapp-08: ⊦ gnd ' + gndx = gndx0 + gnd0 ' ∧ gndx0 ≠ [] → gnd ∈ gndx0 ∧ gnd0 ∈ gndx; (forward) from specification list[group-store]% ⊦ # gndx = 0 ↔ gndx = []; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)