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Proof step 36 from proof transaction-prefix-app-last (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ ¬ n < # ndx → (ndx + ndx0)[n] = ndx0[n - # ndx]
Proof step 38:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = mkgnode(nd1, m, boolvar, boolvar0) ' + gndx0, gndx.head = mkgnode(nd2, m1, boolvar3, boolvar4), gndx[n0] = mkgnode(nd4, m3, boolvar7, boolvar8), gndx[0] = mkgnode(nd5, m4, boolvar9, boolvar10), (mkgnode(nd1, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), 0 < # ndx, gndx ≠ [] → nd5 = (ndx + nd ')[0], mkgnode(nd1, m, boolvar, boolvar0) ∈ gndx ∨ mkgnode(nd1, m, boolvar, boolvar0) = mkgnode(nd, n, ndx = [], true), mkgnode(nd, n, ndx = [], true) = mkgnode(nd1, m, boolvar, boolvar0) ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0, gndx = [] ∨ boolvar3 ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)) ⊦ nd1 = (ndx + nd ')[0]

Rule argument

spec: list-del, inst: node-list name: get-append-grt seq: ⊦ ¬ n < # ndx → (ndx + ndx0)[n] = ndx0[n - # ndx] subst: [n, ndx0, ndx] → [0, nd ', ndx] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ # ndx = 0 ↔ ndx = []; (s)%in-15: ⊦ gndx + gnd ' = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%in-14: ⊦ gnd ' + gndx = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]% ⊦ # [] = 0; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)% ⊦ gnd ∈ gnd0 ' + gndx ↔ gnd = gnd0 ∨ gnd ∈ gndx; (s)% ⊦ gnd ∈ gndx + gndx0 ↔ gnd ∈ gndx ∨ gnd ∈ gndx0; (s)% ⊦ gnd ∈ gnd0 ' ↔ gnd = gnd0; (s)% ⊦ [] + gndx = gndx; (s)% ⊦ gnd ' = gnd0 ' + gndx ↔ gnd = gnd0 ∧ gndx = []; (ws)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ # [] = 0; (s)% ⊦ nd '[0] = nd; (s) Used terms: 0, nd ', ndx