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Proof step 41 from proof transaction-prefix-app-last (previous step)

gndx + mkgnode(nd, n, false, true) ' = mkgnode(nd1, m, boolvar, boolvar0) ' + gndx0, # ndx0 + 1 = # gndx, gndx.head = mkgnode(nd0, m1, true, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd1, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), mkgnode(nd, n, false, true) ∈ gndx0, mkgnode(nd1, m, boolvar, boolvar0) ∈ gndx, ∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ⊦ gndx = [], nd1 = nd0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: list-data, inst: group-store name: elim-list-c seq: gndx ≠ [] ⊦ gnd = gndx.head ∧ gndx0 = gndx.tail ↔ gndx = gnd + gndx0 subst: [gndx, gnd, gndx0] → [gndx, gnd, gndx1]

Additional information

Used simplifier rules: ⊦ gnd + gndx = gnd ' + gndx; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gnd ' + gndx = gnd0 ' + gndx0 ↔ gnd = gnd0 ∧ gndx = gndx0; (ws)% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)%gndx ≠ [] ⊦ gnd = gndx.head ∧ gndx0 = gndx.tail ↔ gndx = gnd + gndx0; (elim) Used terms: gndx, gnd, gndx1