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Proof step 42 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, boolvar3, boolvar4), gndx[n1] = mkgnode(nd5, m4, boolvar9, boolvar10), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx0[n1 - # mkgnode(nd0, m, true, boolvar0) '] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), n1 ≤ # gndx, n1 < # gndx → nd5 = (ndx + nd ')[n1], mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], true), gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd, n, ndx = [], true) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0 ⊦ nd1 = (ndx + nd ')[n1], n1 < # mkgnode(nd0, m, true, boolvar0) '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx[n1] = mkgnode(nd5, m4, boolvar9, boolvar10), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), gndx0[n1 - 1] = mkgnode(nd1, m0, boolvar1, boolvar2), mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx, mkgnode(nd, n, ndx = [], true) ∈ gndx0, n1 ≤ # gndx, n1 < # gndx → nd5 = (ndx + nd ')[n1], ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], n1 = 0, nd1 = (ndx + nd ')[n1]

Rule argument

Additional information

Used simplifier rules: ⊦ gnd ' + gndx = gndx0 + gndx1 → (gnd ∈ gndx0 ↔ gndx0 ≠ []); (ss)%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]% ⊦ m ≤ 0 ↔ m = 0; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ # ndx = 0 ↔ ndx = []; (s)% ⊦ # [] = 0; (s)% ⊦ gnd ' = gnd0 ' + gndx ↔ gnd = gnd0 ∧ gndx = []; (ws)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ [] + gndx = gndx; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ # gnd ' = 0 +1; (s)