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Proof step 29 from proof adr-in-index-node-key (previous step)

# gndx0 = # lax0, # gndx1 = # lax1, (gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1)[# lax0] = mkgnode(nd0, m1, boolvar1, boolvar2), ri[nd0.key] = @(n, n0, n1), gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), # lax0 < valid-group-nodes(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1), # lax0 < #(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1), inv-flashsize(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1), @(n0, n1) ∈ prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1), lax0 + @(n0, n1) ' + lax1), n ∈ gstore, nd0.key ∈ ri ⊦ dups(lax0 + lax1), dups(lax0), dups(lax1), n ∈ ginval, @(n0, n1) ∈ lax0, @(n0, n1) ∈ lax1, nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# gndx1 = # lax1, # gndx0 = # lax0, gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), ri[nd0.key] = @(n, n0, n1), (gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1)[# lax0] = mkgnode(nd0, m1, boolvar1, boolvar2), # lax0 < valid-group-nodes(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1), inv-flashsize(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1), nd0.key ∈ ri, n ∈ gstore, @(n0, n1) ∈ prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1), lax0 + @(n0, n1) ' + lax1) ⊦ dups(lax1), dups(lax0), dups(lax0 + lax1), @(n0, n1) ∈ lax1, @(n0, n1) ∈ lax0, n ∈ ginval, nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

Rule argument

Additional information

Used simplifier rules: valid-group-nodes-ls: ⊦ n < valid-group-nodes(gndx) → n < # gndx;% ⊦ m ≤ m + n; (s)% ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ m +1 = m + 1; (s)% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)