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Proof step 33 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, boolvar3, boolvar4), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx[n1] = mkgnode(nd5, m4, boolvar9, boolvar10), n1 ≤ # gndx, n1 < # gndx → nd5 = (ndx + nd ')[n1], mkgnode(nd, n, ndx = [], true) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0, gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], true) ⊦ nd1 = (ndx + nd ')[n1]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ ¬ n < # gndx → (gndx + gndx0)[n] = gndx0[n - # gndx]
Proof step 35:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, boolvar3, boolvar4), gndx[n1] = mkgnode(nd5, m4, boolvar9, boolvar10), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), n1 < # mkgnode(nd0, m, true, boolvar0) ', n1 ≤ # gndx, n1 < # gndx → nd5 = (ndx + nd ')[n1], mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], true), gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd, n, ndx = [], true) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0 ⊦ nd1 = (ndx + nd ')[n1]
Proof step 42:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd0, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, boolvar3, boolvar4), gndx[n1] = mkgnode(nd5, m4, boolvar9, boolvar10), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx0[n1 - # mkgnode(nd0, m, true, boolvar0) '] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), n1 ≤ # gndx, n1 < # gndx → nd5 = (ndx + nd ')[n1], mkgnode(nd0, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd0, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], true), gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd, n, ndx = [], true) = mkgnode(nd0, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0 ⊦ nd1 = (ndx + nd ')[n1], n1 < # 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] → [n1, gndx0, mkgnode(nd0, m, true, boolvar0) '] flags: <all paths>

Additional information

Used terms: n1, gndx0, mkgnode(nd0, m, true, boolvar0) '