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Proof step 10 from proof transaction-prefix-last-nonend (previous step)

gndx + mkgnode(nd, n, boolvar, true) ' = mkgnode(nd0, m, true, boolvar1) ' + gndx0, (mkgnode(nd0, m, true, boolvar1) ' + gndx0)[# gndx0] = mkgnode(nd1, m0, boolvar0, boolvar2), # gndx + 1 < # ndx, gndx0 ≠ [] ∧ ¬ # gndx < # gndx0 → ¬ boolvar0, ¬ # gndx < # gndx0 → ¬ boolvar2, ∀ n0. ¬ # gndx < n0 → (mkgnode(nd0, m, true, boolvar1) ' + gndx0)[n0].nd = ndx[n0], mkgnode(nd0, m, true, boolvar1) ∈ gndx ∨ mkgnode(nd0, m, true, boolvar1) = mkgnode(nd, n, boolvar, true), mkgnode(nd, n, boolvar, true) = mkgnode(nd0, m, true, boolvar1) ∨ mkgnode(nd, n, boolvar, true) ∈ gndx0 ⊦ ndx = []

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [# gndx0, gndx0, mkgnode(nd0, m, true, boolvar1) '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # gndx → (gndx + gndx0)[n] = gndx[n]; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # gnd ' = 0 +1; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)% ⊦ # [] = 0; (s)% ⊦ gnd '[0] = gnd; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ gndx + [] = gndx; (s)% ⊦ gnd ' = gndx + gnd0 ' ↔ gnd = gnd0 ∧ gndx = []; (ws)% ⊦ ¬ m < 0; (s) Used terms: # gndx0, gndx0, mkgnode(nd0, m, true, boolvar1) '