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Proof step 18 from proof adr-in-index-node-key (previous step)

# groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0).gndlist = # groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0).ladrlist, # gndx1 = # lax1, gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), ri[nodes(gstore ↓, ginval)[@(n, n0, n1)].key] = @(n, n0, n1), inv-flashsize (groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0).gndlist, groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0).ladrlist), @(n0, n1) ∈ prefixn(valid-group-nodes(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1), lax0 + @(n0, n1) ' + lax1), nodes(gstore ↓, ginval)[@(n, n0, n1)].key ∈ ri, n ∈ gstore, nodes(gstore ↓, ginval)[@(n, n0, n1)].key.inode? → nodes(gstore ↓, ginval)[@(n, n0, n1)].inode? ∧ nodes(gstore ↓, ginval)[@(n, n0, n1)].key.ino ≠ 0, nodes(gstore ↓, ginval)[@(n, n0, n1)].key.dentry? → nodes(gstore ↓, ginval)[@(n, n0, n1)].dentry?, nodes(gstore ↓, ginval)[@(n, n0, n1)].key.data? → nodes(gstore ↓, ginval)[@(n, n0, n1)].data? ⊦ dups(groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0).ladrlist), n ∈ ginval, nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# gndx1 = # lax1, # gndx0 = # lax0, gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), ri[nodes(gstore ↓, ginval)[@(n, n0, n1)].key] = @(n, n0, n1), 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), nodes(gstore ↓, ginval)[@(n, n0, n1)].key ∈ ri, n ∈ gstore, nodes(gstore ↓, ginval)[@(n, n0, n1)].key.inode? → nodes(gstore ↓, ginval)[@(n, n0, n1)].inode? ∧ nodes(gstore ↓, ginval)[@(n, n0, n1)].key.ino ≠ 0, nodes(gstore ↓, ginval)[@(n, n0, n1)].key.dentry? → nodes(gstore ↓, ginval)[@(n, n0, n1)].dentry?, nodes(gstore ↓, ginval)[@(n, n0, n1)].key.data? → nodes(gstore ↓, ginval)[@(n, n0, n1)].data? ⊦ 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: a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]%⊦ 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)