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Proof step 25 from proof nodes-transaction (previous step)

# lax = # gndx, # ndx = # gndx1, # lax2 + # lax0 + 1 = # gndx1, gstore[n, groupblock(gndx + gndx1, lax + lax2 + @(m2, m3) ' + lax0, m0)][@(n, m2, m3)] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), transaction(ndx, gndx1), n ∈ gstore ⊦ nd = ndx[pos(@(n, m2, m3), lax2.to-adr(n) + @(n, m2, m3) ' + lax0.to-adr(n))], dups(lax + lax2), dups(lax0), dups(lax2 + lax0), dups((lax + lax2) + lax0), dups(lax), dups(lax2), @(m2, m3) ∈ lax0, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax, n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ¬ adr ∈ ax → pos(adr, ax + ax0) = pos(adr, ax0) + # ax
Proof step 27:
# ndx = # gndx1, # lax = # gndx, # lax2 + # lax0 + 1 = # gndx1, gstore[n] = groupblock(gndx, lax, m), gstore[n, groupblock(gndx + gndx1, lax + lax2 + @(m2, m3) ' + lax0, m0)][@(n, m2, m3)] = mkgnode(nd, m4, boolvar, boolvar0), transaction(ndx, gndx1), n ∈ gstore ⊦ nd = ndx[pos(@(n, m2, m3), @(n, m2, m3) ' + lax0.to-adr(n)) + # lax2.to-adr(n)], dups(lax2), dups(lax), dups((lax + lax2) + lax0), dups(lax2 + lax0), dups(lax0), dups(lax + lax2), n ∈ ginval, @(m2, m3) ∈ lax, @(m2, m3) ∈ lax2, @(m2, m3) ∈ lax0, @(n, m2, m3) ∈ lax2.to-adr(n)

Rule argument

spec: list-del, inst: address-list-set name: app-05-neg seq: ⊦ ¬ adr ∈ ax → pos(adr, ax + ax0) = pos(adr, ax0) + # ax subst: [ax0, ax, adr] → [@(n, m2, m3) ' + lax0.to-adr(n), lax2.to-adr(n), @(n, m2, m3)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ ax → pos(adr, ax + ax0) = pos(adr, ax); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ @(m, m0, m1) ∈ lax.to-adr(n) ↔ m = n ∧ @(m0, m1) ∈ lax; (ws) Used terms: @(n, m2, m3) ' + lax0.to-adr(n), lax2.to-adr(n), @(n, m2, m3)