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Proof step 62 from proof prepost-gc-referenced-nodes (previous step)

# groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m).gndlist = # groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m).ladrlist, # gndx0 = # lax1, # lax = # gndx2, prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2), gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2) [pos(@(m2, m3), lax1 + @(m2, m3) ' + lax) ] = mkgnode(nd0, m4, boolvar1, boolvar2), ri[nd.key] = @(m1, m2, m3), gstore2[m1] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m), inv(gstore2 \ ginval), inv-flashsize (groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m).gndlist, groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m).ladrlist), key-cons(nd.key, nd0), @(m2, m3) ∈ prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2), lax1 + @(m2, m3) ' + lax), nd.key ∈ ri, m1 ∈ gstore2 ⊦ nd = nd0, dups(groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m).ladrlist), m1 ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 63:
# gndx0 = # lax1, # lax = # gndx2, prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2), gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2)[# lax1] = mkgnode(nd0, m4, boolvar1, boolvar2), ri[nd.key] = @(m1, m2, m3), gstore2[m1] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m), inv(gstore2 \ ginval), inv-flashsize(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax), key-cons(nd.key, nd0), @(m2, m3) ∈ prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2), lax1 + @(m2, m3) ' + lax), nd.key ∈ ri, m1 ∈ gstore2 ⊦ nd = nd0, dups(lax), dups(lax1), dups(lax1 + lax), @(m2, m3) ∈ lax, @(m2, m3) ∈ lax1, m1 ∈ ginval

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]% ⊦ n + 0 = n; (s)% ⊦ pos(ladr, ladr ' + lax) = 0; (s)% ⊦ ¬ ladr ∈ lax → pos(ladr, lax + lax0) = pos(ladr, lax0) + # lax; (s)%⊦ dups(lax + ladr ' + lax0) ↔ ladr ∈ lax ∨ ladr ∈ lax0 ∨ dups(lax + lax0); (ws)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ #(ladr ' + lax) = (# lax)+1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (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)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)