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Proof step 45 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), (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(nd4, m3, boolvar7, boolvar8), n1 ≤ # gndx, n1 < # gndx → nd4 = (ndx + nd ' + ndx1)[n1], mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], false), gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd, n, ndx = [], false) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], false) ∈ gndx0 ⊦ nd1 = (ndx + nd ' + ndx1)[n1], ndx1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del, inst: node-list name: get-append-grt seq: ⊦ ¬ n < # ndx → (ndx + ndx0)[n] = ndx0[n - # ndx] subst: [n, ndx0, ndx] → [n1, nd ' + ndx1, ndx] flags: <all paths>

Additional information

Used terms: n1, nd ' + ndx1, ndx