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Proof step 102 from proof inv-addn (previous step)

# lax = # gndx, # lax0 = # gndx0, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro1 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro1, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro0, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(groupblock(gndx0 + gndx, lax0 + lax, m0)), inv(gstore1), inv(gstore2 \ jro1), inv(gstore3 \ jro0), inv(groupblock(gndx0, lax0, m0)), inv-flashsize(gndx, lax), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), transaction(ndx, gndx), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, dom gstore2 ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ abs-log(nx0.butlast, gstore3 ↓) + lax0.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓), gndx = [], nx0 = [], pmaxino = 0, dups(lax), dups(nx1), dups(nx0)

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 4 flags: rotate, discard

Additional information

Used simplifier rules: ⊦ nx ≠ [] → ( abs-log(nx, gstore) = abs-log(nx.butlast, gstore) + ax ↔ ax = gstore[nx.last].ladrlist.to-adr(nx.last)); (s)% ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓; (s)% ⊦ lax0.to-adr(n) = lax1.to-adr(n) ↔ lax0 = lax1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0); (s)%⊦ valid-journal-head(nx, gstore, ginval) ∧ nx ≠ [] ∧ gstore[nx.last] = groupblock(gndx, lax, lnum) → valid-group-nodes(gndx) = # gndx; (s)% ⊦ prefixn(# gndx, gndx) = gndx; (s)% ⊦ inv(groupblock(gndx, lax, m0)) → prefixn(# gndx, lax) = lax; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)