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Proof step 43 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, 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]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), gndx0[m5] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), gndx[n1] = mkgnode(nd5, m4, boolvar9, boolvar10), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), n1 = m5 + 1, mkgnode(nd, n, ndx = [], true) ∈ gndx0, mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx, 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

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n1, m5]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n1, m5