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Proof step 26 from proof adr-in-index-node-key (previous step)

# gndx1 = # lax1, # gndx0 = # lax0, gstore ↓[@(n, n0, n1).lnum].gndlist[pos(@(@(n, n0, n1).pos, @(n, n0, n1).size), gstore ↓[@(n, n0, n1).lnum].ladrlist)] = mkgnode(nd0, m1, boolvar1, boolvar2), gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), ri[nd0.key] = @(n, n0, n1), 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), @(n, n0, n1) ∈ gstore ↓ ⊦ dups(lax1), dups(lax0), dups(lax0 + lax1), @(n0, n1) ∈ lax1, @(n0, n1) ∈ lax0, n ∈ ginval, nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# 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), prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1), gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1)[# lax0] = mkgnode(nd0, m1, boolvar1, boolvar2), 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: down-store-at: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓;%down-store-adr-in-explicit: ⊦ @(m0, m1, m2) ∈ gstore ↓ ↔ m0 ∈ gstore ∧ @(m1, m2) ∈ gstore ↓[m0].ladrlist;%down-block-explicit: ⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0);%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ pos(ladr, ladr ' + lax) = 0; (s)% ⊦ ¬ ladr ∈ lax → pos(ladr, lax + lax0) = pos(ladr, lax0) + # lax; (s)%⊦ ladr ∈ prefixn(n, lax) → pos(ladr, prefixn(n, lax)) = pos(ladr, lax); (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ @(m, m0, m1).lnum = m; (s)