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Proof step 10 from proof transaction-prefix-is-transaction-prefix (previous step)

# gndx0 + 1 = # ndx, prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0).head = mkgnode(nd1, m1, boolvar2, boolvar3), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd0, m0, boolvar, boolvar1), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), (mkgnode(nd, m, true, boolvar0) ' + gndx0).last.end, n < # ndx, n ≤ # gndx0, ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2], ∀ n2. (n2 ≠ 0 ∧ n2 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].start) ∧ (n2 + 1 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].end) ⊦ ndx = [], (prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0) = [] ∨ boolvar2 ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4) ∧ (n0 < n → ¬ boolvar5)) ∧ (n1 < n → nd0 = ndx[n1])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
# gndx0 + 1 = # ndx, prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0).head = mkgnode(nd1, m1, boolvar2, boolvar3), (mkgnode(nd, m, true, boolvar0) ' + gndx0).last = mkgnode(nd3, m3, boolvar6, boolvar7), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n0] = mkgnode(nd2, m2, boolvar4, boolvar5), prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0)[n1] = mkgnode(nd0, m0, boolvar, boolvar1), boolvar7, n < # ndx, n ≤ # gndx0, ∀ n2. (n2 ≠ 0 ∧ n2 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].start) ∧ (n2 + 1 < # ndx → ¬ (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].end), ∀ n2. n2 < # ndx → (mkgnode(nd, m, true, boolvar0) ' + gndx0)[n2].nd = ndx[n2] ⊦ ndx = [], (prefixn(n, mkgnode(nd, m, true, boolvar0) ' + gndx0) = [] ∨ boolvar2 ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4) ∧ (n0 < n → ¬ boolvar5)) ∧ (n1 < n → nd0 = ndx[n1])

Rule argument

spec: groupnode name: elim seq: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0) subst: [gnd, nd, m, boolvar, boolvar0] → [(mkgnode(nd, m, true, boolvar0) ' + gndx0).last, nd3, m3, boolvar6, boolvar7]

Additional information

Used simplifier rules: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0); (elim) Used terms: (mkgnode(nd, m, true, boolvar0) ' + gndx0).last, nd3, m3, boolvar6, boolvar7