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Proof step 4 from proof transaction-prefix-app-last (previous step)

# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = gnd + gndx0, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ')[n], gndx = [] ∨ gndx.head.start ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)) ⊦ gndx + mkgnode(nd, n, ndx = [], true) ' = [], gnd.start ∧ (n0 ≠ 0 ∧ ¬ # gndx < n0 → ¬ (gndx + mkgnode(nd, n, ndx = [], true) ')[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ∧ (¬ # gndx < n1 → (gndx + mkgnode(nd, n, ndx = [], true) ')[n1].nd = (ndx + nd ')[n1])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# ndx = # gndx, gndx + mkgnode(nd, n, ndx = [], true) ' = gnd ' + gndx0, ∀ n. n < # gndx → gndx[n].nd = (ndx + nd ')[n], gndx = [] ∨ gndx.head.start ∧ (∀ n0. (n0 ≠ 0 ∧ n0 < # gndx → ¬ gndx[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end)), mkgnode(nd, n, ndx = [], true) = gnd ∨ mkgnode(nd, n, ndx = [], true) ∈ gndx0, gnd ∈ gndx ∨ gnd = mkgnode(nd, n, ndx = [], true) ⊦ gnd.start ∧ (n0 ≠ 0 ∧ ¬ # gndx < n0 → ¬ (gnd ' + gndx0)[n0].start) ∧ (n0 < # gndx → ¬ gndx[n0].end) ∧ (¬ # gndx < n1 → (gnd ' + gndx0)[n1].nd = (ndx + nd ')[n1])

Rule argument

Additional information

Used simplifier rules: ⊦ gnd ∈ gnd0 ' ↔ gnd = gnd0; (s)% ⊦ gnd ∈ gndx + gndx0 ↔ gnd ∈ gndx ∨ gnd ∈ gndx0; (s)% ⊦ gnd ∈ gnd0 ' + gndx ↔ gnd = gnd0 ∨ gnd ∈ gndx; (s)%in-14: ⊦ gnd ' + gndx = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]%in-15: ⊦ gndx + gnd ' = gndx0 → gnd ∈ gndx0; (forward) from specification list[group-store]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx + gnd ' ≠ []; (s)% ⊦ gnd + gndx = gnd ' + gndx; (s)