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Proof step 46 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx[m5 + 1] = mkgnode(nd5, m4, boolvar9, boolvar10), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), gndx0[m5] = mkgnode(nd1, m0, boolvar1, boolvar2), gnd = mkgnode(nd2, m1, true, boolvar4), gndx = gnd + gndx1, m5 < # gndx, mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx, mkgnode(nd, n, ndx = [], true) ∈ gndx0, m5 + 1 < # gndx → nd5 = (ndx + nd ')[m5 + 1], ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = (ndx + nd ')[m5 + 1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
# ndx = # gndx1 + 1, (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx1[m5] = mkgnode(nd5, m4, boolvar9, boolvar10), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], true) ')[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (gndx1 + mkgnode(nd, n, ndx = [], true) ')[m5] = mkgnode(nd1, m0, boolvar1, boolvar2), m5 ≤ # gndx1, m5 < # gndx1 → nd5 = (ndx + nd ')[m5 + 1], ∀ n1. (n1 ≠ 0 ∧ ¬ # gndx1 < n1 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n1].start) ∧ (¬ # gndx1 < n1 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n1].end) ⊦ nd1 = (ndx + nd ')[m5 + 1]

Rule argument

Additional information

Used simplifier rules: ⊦ gnd ∈ gnd0 ' ↔ gnd = gnd0; (s)% ⊦ gnd ∈ gndx + gndx0 ↔ gnd ∈ gndx ∨ gnd ∈ gndx0; (s)%in-15: ⊦ gndx + gnd ' = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ gnd ∈ gnd0 ' + gndx ↔ gnd = gnd0 ∨ gnd ∈ gndx; (s)% ⊦ gnd ' + gndx ≠ []; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ m +1 = m + 1; (s)% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ gnd ' + gndx = gnd0 ' + gndx0 ↔ gnd = gnd0 ∧ gndx = gndx0; (ws)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ (gnd ' + gndx)[n + 1] = gndx[n]; (s)% ⊦ gnd + gndx = gnd ' + gndx; (s)