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Proof step 47 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(valid-group-nodes(gndx), gndx)[pos(@(m1, m2), lax + ladr ')] = mkgnode(nd1, m4, boolvar3, boolvar4), pos(@(m1, m2), lax) < # lax, pos(@(m1, m2), lax) < valid-group-nodes(gndx), @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax + ladr '), n ∈ gstore, @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), n0 ≤ m0, valid-group-nodes(gndx) ≤ # gndx ⊦ lax = [], nd0 = nd1, n ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
# gndx = # lax, prefixn(valid-group-nodes(gndx), gndx)[pos(@(m1, m2), lax + ladr ')] = mkgnode(nd1, m4, boolvar3, boolvar4), gndx[pos(@(m1, m2), lax)] = mkgnode(nd0, m, boolvar1, boolvar2), gstore[n] = groupblock(gndx, lax, n0), pos(@(m1, m2), lax) < valid-group-nodes(gndx), pos(@(m1, m2), lax) < # lax, n ∈ gstore, @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), valid-group-nodes(gndx) ≤ # lax, n0 ≤ m0 ⊦ lax = [], nd0 = nd1, n ∈ ginval

Rule argument

Additional information

Used simplifier rules: valid-group-nodes-ls: ⊦ n < valid-group-nodes(gndx) → n < # gndx;%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%n ≤ # lax ⊦ prefixn(n, lax + lax0) = prefixn(n, lax); (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m +1 = m + 1; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)