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Proof step 15 from proof transaction-prefix-app (previous step)

((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n0] = mkgnode(ndx[n0], m0, boolvar1, boolvar2), (mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n0] = mkgnode(nd, m, boolvar, boolvar0), (mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n] = mkgnode(nd2, m2, boolvar5, boolvar6), (# gndx2 + 1) + # gndx1 < # ndx, # gndx2 + 1 < # ndx, n0 < # ndx, n0 + 1 < # ndx, n0 ≤ # gndx2, n0 ≤ # gndx2 + # gndx1, ∀ n1. (n1 ≠ 0 ∧ ¬ # gndx2 + # gndx1 < n1 → ¬ ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].start) ∧ (¬ # gndx2 + # gndx1 < n1 → ¬ ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].end) ⊦ nd = ndx[n0], ndx = []

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(nd1, m1, true, boolvar4) ' + gndx2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n < # gndx → (gndx + gndx0)[n] = gndx[n]; (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: n0, gndx1, mkgnode(nd1, m1, true, boolvar4) ' + gndx2