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Proof step 41 from proof nodes-append-subseteq (previous step)

# gndx = # lax, gstore[n] = groupblock(gndx, lax, n0), gndx[pos(@(m1, m2), lax)] = mkgnode(nd0, m, boolvar1, boolvar2), prefixn(# lax + 1, gndx + mkgnode(nd, m3, boolvar, boolvar0) ')[pos(@(m1, m2), lax + ladr ')] = mkgnode(nd1, m4, boolvar3, boolvar4), boolvar0, pos(@(m1, m2), lax) < # lax, pos(@(m1, m2), lax) < valid-group-nodes(gndx), @(m1, m2) ∈ prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), n ∈ gstore, @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), n0 ≤ m0 ⊦ lax = [], nd0 = nd1, n ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# gndx = # lax, gstore[n] = groupblock(gndx, lax, n0), gndx[pos(@(m1, m2), lax)] = mkgnode(nd0, m, boolvar1, boolvar2), (gndx + mkgnode(nd, m3, boolvar, true) ')[pos(@(m1, m2), lax)] = mkgnode(nd1, m4, boolvar3, boolvar4), pos(@(m1, m2), lax) < valid-group-nodes(gndx), n ∈ gstore, @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), @(m1, m2) ∈ lax, n0 ≤ m0 ⊦ lax = [], nd0 = nd1, n ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ ladr ∈ lax → pos(ladr, lax) < # lax; (s)% ⊦ ladr ∈ lax → pos(ladr, lax + lax0) = pos(ladr, lax); (s)% ⊦ ¬ ladr ∈ lax → ¬ ladr ∈ prefixn(n, lax); (s)% ⊦ ¬ ladr ∈ lax → pos(ladr, lax + lax0) = pos(ladr, lax0) + # lax; (s)% ⊦ ¬ ladr ∈ lax → pos(ladr, lax) = # lax; (s)% ⊦ ladr ∈ ladr0 ' ↔ ladr = ladr0; (s)% ⊦ ladr ∈ lax + lax0 ↔ ladr ∈ lax ∨ ladr ∈ lax0; (s)%# lax ≤ m ⊦ prefixn(m, lax) = lax; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ # ladr ' = 0 +1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s)% ⊦ ¬ n < n; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ # gnd ' = 0 +1; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)