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Proof step 31 from proof nodes-cons-write-app (previous step)

# gndx0 = # lax0 + # lax2, # ndx = # lax0 + # lax2 + 1, # gndx1 = # lax1, (mkgnode(nd, m1, true, boolvar0) ' + gndx0).last = mkgnode(nd0, m2, boolvar1, true), (mkgnode(nd, m1, true, boolvar0) ' + gndx0)[# lax0] = mkgnode(nd1, m3, boolvar, boolvar2), gstore[m6] = groupblock(gndx1, lax1, m9), # lax0 < # mkgnode(nd, m1, true, boolvar0) ', 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) ⊦ 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 32:
# ndx = 1 + # lax2, # gndx0 = # lax2, # gndx1 = # lax1, (mkgnode(nd1, m1, true, boolvar0) ' + gndx0).last = mkgnode(nd0, m2, boolvar1, true), gstore[m6] = groupblock(gndx1, lax1, m9), m6 ∈ gstore, ∀ n0. (n0 ≠ 0 ∧ ¬ # lax2 < n0 → ¬ (mkgnode(nd1, m1, true, boolvar0) ' + gndx0)[n0].start) ∧ (n0 < # lax2 → ¬ (mkgnode(nd1, m1, true, boolvar0) ' + gndx0)[n0].end), ∀ n0. ¬ # lax2 < n0 → (mkgnode(nd1, m1, true, boolvar0) ' + gndx0)[n0].nd = ndx[n0] ⊦ nd1 = ndx[0], dups(lax2), dups(lax1), dups(lax1 + lax2), m6 ∈ ginval, @(m7, m8) ∈ lax1, @(m7, m8) ∈ lax2

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]% ⊦ ¬ ladr ∈ []; (s)% ⊦ ¬ dups([]); (s)% ⊦ lax + [] = lax; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ [] + lax = lax; (s)% ⊦ 0 ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%⊦ mkgnode(nd, m, boolvar, boolvar0) = mkgnode(nd0, m0, boolvar1, boolvar2) ↔ nd = nd0 ∧ m = m0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2); (ws)% ⊦ gnd '[0] = gnd; (s)% ⊦ # [] = 0; (s)% ⊦ # lax = 0 ↔ lax = []; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ # gnd ' = 0 +1; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ n < # gndx → (gndx + gndx0)[n] = gndx[n]; (s)