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Proof step 31 from proof transaction-prefix-app-nonlast (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], false) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, true), gndx[n0] = mkgnode(nd4, m3, boolvar3, boolvar6), n0 ≤ # gndx, n0 < # gndx → ¬ boolvar6, n0 ≠ 0 ∧ n0 < # gndx → ¬ boolvar3, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ' + ndx1)[n], mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], false), mkgnode(nd, n, ndx = [], false) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], false) ∈ gndx0 ⊦ ndx1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ ¬ n < # gndx → (gndx + gndx0)[n] = gndx0[n - # gndx]
Proof step 33:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], false) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar3, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, true), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), n0 < # mkgnode(nd0, m, true, boolvar0) ', n0 ≤ # gndx, n0 ≠ 0 ∧ n0 < # gndx → ¬ boolvar3, n0 < # gndx → ¬ boolvar6, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ' + ndx1)[n], mkgnode(nd, n, ndx = [], false) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], false) ∈ gndx0, mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], false) ⊦ ndx1 = []
Proof step 35:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], false) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, true, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar3, boolvar6), gndx0[n0 - # mkgnode(nd0, m, true, boolvar0) '] = mkgnode(nd3, m2, boolvar5, true), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), n0 ≤ # gndx, n0 ≠ 0 ∧ n0 < # gndx → ¬ boolvar3, n0 < # gndx → ¬ boolvar6, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ' + ndx1)[n], mkgnode(nd, n, ndx = [], false) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], false) ∈ gndx0, mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], false) ⊦ ndx1 = [], n0 < # mkgnode(nd0, m, true, boolvar0) '

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, gndx0, mkgnode(nd0, m, true, boolvar0) '] flags: <all paths>

Additional information

Used terms: n0, gndx0, mkgnode(nd0, m, true, boolvar0) '