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Proof step 47 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx1 + 1, (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx1[m5] = mkgnode(nd5, m4, boolvar9, boolvar10), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], true) ')[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (gndx1 + mkgnode(nd, n, ndx = [], true) ')[m5] = mkgnode(nd1, m0, boolvar1, boolvar2), m5 ≤ # gndx1, m5 < # gndx1 → nd5 = (ndx + nd ')[m5 + 1], ∀ n1. (n1 ≠ 0 ∧ ¬ # gndx1 < n1 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n1].start) ∧ (¬ # gndx1 < n1 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n1].end) ⊦ nd1 = (ndx + nd ')[m5 + 1]

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] → [m5, mkgnode(nd, n, ndx = [], true) ', 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)% ⊦ # [] = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # gndx = 0 ↔ gndx = []; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n = # ndx → (ndx + nd ')[n] = nd; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ n < # gndx → (gndx + gnd ')[n] = gndx[n]; (s)% ⊦ m < n → m ≤ n; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic Used terms: m5, mkgnode(nd, n, ndx = [], true) ', gndx1