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Proof step 35 from proof nodes-cons-write-app (previous step)

# gndx0 = # lax0 + # lax2, # ndx = # lax0 + # lax2 + 1, # gndx1 = # lax1, # lax0 = m + 1, (mkgnode(nd, m1, true, boolvar0) ' + gndx0).last = mkgnode(nd0, m2, boolvar1, true), gndx0[m] = mkgnode(nd1, m3, boolvar, boolvar2), gstore[m6] = groupblock(gndx1, lax1, m9), m6 ∈ gstore, # lax0 ≤ # gndx0, ∀ n0. ¬ # gndx0 < n0 → (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].nd = ndx[n0], ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].end) ⊦ # lax0 = 0, lax0 = [], nd1 = ndx[# lax0], dups((lax1 + lax0) + lax2), dups(lax1), dups(lax0 + lax2), dups(lax1 + lax0), dups(lax2), dups(lax0), @(m7, m8) ∈ lax2, @(m7, m8) ∈ lax0, @(m7, m8) ∈ lax1, m6 ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# gndx0 = (m + 1) + # lax2, # ndx = 2 + m + # lax2, # gndx1 = # lax1, # lax0 = m + 1, gndx0.last = mkgnode(nd0, m2, boolvar1, true), gndx0[m] = mkgnode(nd1, m3, boolvar, boolvar2), gstore[m6] = groupblock(gndx1, lax1, m9), m < # gndx0, m6 ∈ gstore, ∀ n0. ¬ # gndx0 < n0 → (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].nd = ndx[n0], ∀ n0. (n0 ≠ 0 ∧ ¬ # gndx0 < n0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].start) ∧ (n0 < # gndx0 → ¬ (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[n0].end) ⊦ gndx0 = [], lax0 = [], nd1 = ndx[m + 1], dups((lax1 + lax0) + lax2), dups(lax1), dups(lax0 + lax2), dups(lax1 + lax0), dups(lax2), dups(lax0), @(m7, m8) ∈ lax2, @(m7, m8) ∈ lax0, @(m7, m8) ∈ lax1, m6 ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ m + n < m; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx ≠ [] → (gnd ' + gndx).last = gndx.last; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%eqle-one: ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat% ⊦ m + 1 ≤ n ↔ m < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # lax = 0 ↔ lax = []; (s)