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Proof step 52 from proof transaction-prefix-app-nonlast (previous step)

# ndx = # gndx1 + 1, (gndx1 + mkgnode(nd, n, ndx = [], false) ')[n1 - # mkgnode(nd0, m, true, boolvar0) '] = mkgnode(nd1, m0, boolvar1, boolvar2), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n1] = mkgnode(ndx[n1], m3, boolvar7, boolvar8), n1 ≤ # gndx1, ∀ n2. (n2 ≠ 0 ∧ ¬ # gndx1 < n2 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].start) ∧ (¬ # gndx1 < n2 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].end) ⊦ nd1 = ndx[n1], ndx1 = [], n1 < # mkgnode(nd0, m, true, boolvar0) '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
# ndx = # gndx1 + 1, gndx1[n1 - 1] = mkgnode(ndx[n1], m3, boolvar7, boolvar8), (mkgnode(nd0, m, true, boolvar0) ' + gndx1 + mkgnode(nd, n, ndx = [], false) ')[n0] = mkgnode(nd3, m2, boolvar5, boolvar6), (gndx1 + mkgnode(nd, n, ndx = [], false) ')[n1 - 1] = mkgnode(nd1, m0, boolvar1, boolvar2), n1 ≤ # gndx1, ∀ n2. (n2 ≠ 0 ∧ ¬ # gndx1 < n2 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].start) ∧ (¬ # gndx1 < n2 → ¬ (mkgnode(nd0, m, true, boolvar0) ' + gndx1)[n2].end) ⊦ n1 = 0, nd1 = ndx[n1], ndx1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < 1 ↔ m = 0; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # gnd ' = 0 +1; (s)% ⊦ ¬ n < # gndx → (gndx + gndx0)[n] = gndx0[n - # gndx]; (s)