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Proof step 45 from proof refine-remove (previous step)

gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)][n] = groupblock(gndx0, lax0, m2), ri[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + m1), remove-refsize0(gstore1) = gstore1, gstore2[n] ↓ = groupblock(gndx1, lax1, m3), elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro0), inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-inj(ri), ri-inj(ri -- key), ri-inj(fi1), m ∈ gstore2, key ∈ ri, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid2 → jvalid0 ⊦ abs-log(nx, gstore2 ↓) = abs-log(nx, gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]), jmaxino = 0, pmaxino = 0, dups(nx), (n ∈ gstore2 → n ∈ gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]) ∧ (n ∈ gstore2 → gndx0 = gndx1 ∧ lax0 = lax1)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: n = m

Additional information

Used simplifier rules: ⊦ n ≠ n0 → gstore[n0, gblock][n] = gstore[n]; (s)% ⊦ n ≠ n0 → (n ∈ gstore[n0, gblock] ↔ n ∈ gstore); (s)% ⊦ n ∈ gstore ↓ ↔ n ∈ gstore; (s)% ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓; (s)%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws)% ⊦ gstore[n, gblock][n] = gblock; (s)% ⊦ n ∈ gstore[n, gblock]; (s)%⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0); (s) Used formulas: n = m