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Proof step 19 from proof transaction-prefix-app (previous step)

gndx0[n] = mkgnode(nd2, m2, boolvar5, boolvar6), gndx0[n0] = mkgnode(nd, m, boolvar, boolvar0), gnd = mkgnode(nd1, m1, true, boolvar4), gndx0 = gnd + gndx2, # gndx0 < # ndx, # gndx0 + # gndx1 < # ndx, ∀ n. n < # gndx0 + # gndx1 → (gndx0 + gndx1)[n].nd = ndx[n], ∀ n. (n ≠ 0 ∧ n < # gndx0 + # gndx1 → ¬ (gndx0 + gndx1)[n].start) ∧ (n < # gndx0 + # gndx1 → ¬ (gndx0 + gndx1)[n].end) ⊦ gndx0 + gndx1 = [], gndx0 = [], ndx = [], (n < # gndx0 → ¬ boolvar6) ∧ (n ≠ 0 ∧ n < # gndx0 → ¬ boolvar5)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
(mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n0] = mkgnode(nd, m, boolvar, boolvar0), (mkgnode(nd1, m1, true, boolvar4) ' + gndx2)[n] = mkgnode(nd2, m2, boolvar5, boolvar6), (# gndx2 + 1) + # gndx1 < # ndx, # gndx2 + 1 < # ndx, ∀ n1. (n1 ≠ 0 ∧ ¬ # gndx2 + # gndx1 < n1 → ¬ ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].start) ∧ (¬ # gndx2 + # gndx1 < n1 → ¬ ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].end), ∀ n1. ¬ # gndx2 + # gndx1 < n1 → ((mkgnode(nd1, m1, true, boolvar4) ' + gndx2) + gndx1)[n1].nd = ndx[n1] ⊦ ndx = [], (¬ # gndx2 < n → ¬ boolvar6) ∧ (n ≠ 0 ∧ ¬ # gndx2 < n → ¬ boolvar5)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gnd ' + gndx ≠ []; (s)% ⊦ gnd + gndx = gnd ' + gndx; (s)