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Proof step 12 from proof transaction-prefix-last-nonend (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
gndx + mkgnode(nd, n, boolvar, true) ' = mkgnode(nd0, m, true, boolvar1) ' + gndx0, gndx0[# gndx0 - 1] = mkgnode(nd1, m0, boolvar0, boolvar2), # gndx + 1 < # ndx, mkgnode(nd0, m, true, boolvar1) ∈ gndx, mkgnode(nd, n, boolvar, true) ∈ gndx0, ¬ # gndx < # gndx0 → ¬ boolvar0, ¬ # gndx < # gndx0 → ¬ boolvar2, ∀ n0. ¬ # gndx < n0 → (mkgnode(nd0, m, true, boolvar1) ' + gndx0)[n0].nd = ndx[n0] ⊦ gndx0 = [], ndx = []

Rule argument

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%inapp-07: ⊦ gnd ' + gndx = gndx0 + gnd0 ' ∧ gndx ≠ [] → gnd ∈ gndx0 ∧ gnd0 ∈ gndx; (forward) from specification list[group-store]% ⊦ # gndx = 0 ↔ gndx = []; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ # gnd ' = 0 +1; (s)