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Proof step 47 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, boolvar3, boolvar4), gndx[n1] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), n1 < # ndx, n1 ≤ # gndx, n1 < # gndx → nd4 = (ndx + nd ' + ndx1)[n1], mkgnode(nd, n, ndx = [], false) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], false) ∈ gndx0, gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], false) ⊦ nd1 = (ndx + nd ' + ndx1)[n1], ndx1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
# 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, boolvar6), gndx[n1] = mkgnode(ndx[n1], m3, boolvar7, boolvar8), n1 < # gndx, mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx, mkgnode(nd, n, ndx = [], false) ∈ gndx0, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = ndx[n1], 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]% ⊦ m < n → m ≤ n; (s)% ⊦ # 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%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ n < # ndx → (ndx + ndx0)[n] = ndx[n]; (s)