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Proof step 31 from proof nodes-transaction (previous step)

# ndx = # gndx1, # lax = # gndx, # lax2 + # lax0 + 1 = # gndx1, gstore[n] = groupblock(gndx, lax, m), gndx1[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), transaction(ndx, gndx1), n ∈ gstore ⊦ nd = ndx[# lax2], 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ transaction(ndx, gndx) ↔ # gndx = # ndx ∧ (gndx = [] ∨ gndx.head.start ∧ gndx.last.end ∧ (∀ n. (0 < n ∧ n < # gndx → ¬ gndx[n].start) ∧ (n + 1 < # gndx → ¬ gndx[n].end))) ∧ (∀ n. n < # gndx → gndx[n].nd = ndx[n])
Proof step 33:
# lax = # gndx, # ndx = # gndx1, # lax2 + # lax0 + 1 = # gndx1, gndx1[# lax2] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), n ∈ gstore, ∀ n. n < # gndx1 → gndx1[n].nd = ndx[n], gndx1 = [] ∨ gndx1.head.start ∧ gndx1.last.end ∧ (∀ n. (0 < n ∧ n < # gndx1 → ¬ gndx1[n].start) ∧ (n + 1 < # gndx1 → ¬ gndx1[n].end)) ⊦ nd = ndx[# lax2], 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

Rule argument

spec: gjournal-base name: transaction seq: ⊦ transaction(ndx, gndx) ↔ # gndx = # ndx ∧ ( gndx = [] ∨ gndx.head.start ∧ gndx.last.end ∧ (∀ n. (0 < n ∧ n < # gndx → ¬ gndx[n].start) ∧ (n + 1 < # gndx → ¬ gndx[n].end))) ∧ (∀ n. n < # gndx → gndx[n].nd = ndx[n]) subst: [gndx, ndx] → [gndx1, ndx] flags: <all paths>

Additional information

Used terms: gndx1, ndx