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Proof step 19 from proof transaction-prefix-app-nonlast (previous step)

# ndx = # gndx1 + 1, (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n0] = mkgnode(nd3, m2, true, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n0] = mkgnode(nd2, m1, boolvar, boolvar3), n0 ≤ # ndx, ¬ # gndx1 < n0 → ¬ boolvar, ¬ # gndx1 < n0 → ¬ boolvar3, ∀ n2. ¬ # gndx1 < n2 → (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].nd = (ndx + nd ' + ndx1)[n2] ⊦ n0 = 0, 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] → [n0, gndx1, mkgnode(nd0, m, true, boolvar0) '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # gndx → (gndx + gndx0)[n] = gndx[n]; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # gnd ' = 0 +1; (s)% ⊦ m < 1 ↔ m = 0; (s) Used terms: n0, gndx1, mkgnode(nd0, m, true, boolvar0) '