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Proof step 40 from proof transaction-prefix-app-nonlast (previous step)

# ndx = # gndx1 + 1, gndx1[m4] = mkgnode(nd4, m3, boolvar3, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (gndx1 + mkgnode(nd, n, ndx = [], false) ')[m4] = mkgnode(nd3, m2, boolvar5, true), m4 ≤ # gndx1, m4 < # gndx1 → ¬ boolvar6, m4 < # gndx1 → ¬ boolvar3, ∀ n0. ¬ # gndx1 < n0 → (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n0].nd = (ndx + nd ' + ndx1)[n0] ⊦ 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] → [m4, mkgnode(nd, n, ndx = [], false) ', gndx1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m - 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)% ⊦ n < # gndx → (gndx + gnd ')[n] = gndx[n]; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ m < n → m ≤ n; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic Used terms: m4, mkgnode(nd, n, ndx = [], false) ', gndx1