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Proof step 50 from proof transaction-prefix-app-nonlast (previous step)

# ndx = # gndx1 + 1, (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n1] = mkgnode(ndx[n1], m3, boolvar7, boolvar8), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), n1 ≤ # gndx1, ∀ n2. (n2 ≠ 0 ∧ ¬ # gndx1 < n2 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].start) ∧ (¬ # gndx1 < n2 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].end) ⊦ nd1 = ndx[n1], ndx1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del, inst: group-store name: get-append-grt seq: ⊦ ¬ n < # gndx → (gndx + gndx0)[n] = gndx0[n - # gndx] subst: [n, gndx0, gndx] → [n1, gndx1 + mkgnode(nd, n, ndx = [], false) ', mkgnode(nd0, m, true, boolvar0) '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # gndx → (gndx + gndx0)[n] = gndx[n]; (s)% ⊦ # gnd ' = 0 +1; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ gnd '[0] = gnd; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store] Used terms: n1, gndx1 + mkgnode(nd, n, ndx = [], false) ', mkgnode(nd0, m, true, boolvar0) '