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Proof step 14 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), (mkgnode(nd, m, true, boolvar0) ' + gndx0).last = mkgnode(nd3, m3, boolvar6, true), 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), 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) ⊦ n = 0, ndx = [], boolvar2 ∧ (n0 ≠ 0 ∧ n0 < n → ¬ boolvar4) ∧ (n0 < n → ¬ boolvar5)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-prefixn, inst: group-store name: prefixn-shift-right seq: ⊦ # gndx ≤ n → prefixn(n, gndx + gndx0) = gndx + prefixn(n - # gndx, gndx0) subst: [gndx0, gndx, n] → [gndx0, mkgnode(nd, m, true, boolvar0) ', n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # gnd ' = 0 +1; (s)% ⊦ m ≠ 0 → (m ≤ 1 ↔ m = 1); (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ m ≠ 0 → (1 < m ↔ m ≠ 1); (ss)%n ≤ # gndx ⊦ prefixn(n, gndx + gndx0) = prefixn(n, gndx); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gnd '.head = gnd; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws) Used terms: gndx0, mkgnode(nd, m, true, boolvar0) ', n