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Proof step 38 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd1, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, boolvar3, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx[0] = mkgnode(nd5, m4, boolvar9, boolvar10), (mkgnode(nd1, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), 0 < # ndx, gndx ≠ [] → nd5 = (ndx + nd ')[0], mkgnode(nd1, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd1, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], true), mkgnode(nd, n, ndx = [], true) = mkgnode(nd1, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0, gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)) ⊦ nd1 = (ndx + nd ')[0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
# ndx = # gndx, gndx + mkgnode(nd, n, false, true) ' = mkgnode(nd1, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode((ndx + nd ')[0], m1, true, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd1, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), mkgnode(nd, n, false, true) ∈ gndx0, mkgnode(nd1, m, boolvar, boolvar0) ∈ gndx, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = ndx.head, ndx = []

Rule argument

Additional information

Used simplifier rules: ⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)%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]% ⊦ gnd ' + gndx = gndx0 + gndx1 → (gnd ∈ gndx0 ↔ gndx0 ≠ []); (ss)% ⊦ gndx ≠ [] → gndx[0] = gndx.head; (s)% ⊦ # [] = 0; (s)% ⊦ gnd ∈ gnd0 ' ↔ gnd = gnd0; (s)% ⊦ gnd ∈ gndx + gndx0 ↔ gnd ∈ gndx ∨ gnd ∈ gndx0; (s)% ⊦ gnd ∈ gnd0 ' + gndx ↔ gnd = gnd0 ∨ gnd ∈ gndx; (s)%in-14: ⊦ gnd ' + gndx = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%in-15: ⊦ gndx + gnd ' = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]% ⊦ ndx ≠ [] → ndx[0] = ndx.head; (s)% ⊦ # ndx = 0 ↔ ndx = []; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ n < # ndx → (ndx + nd ')[n] = ndx[n]; (s)