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Proof step 24 from proof btree-sub-clean-write-branches (previous step)

(r2 = r ⊃ mkznode(r0, zbrar[n, mkzbranch(key, adr, zbrar[n].child)], false, boolvar0, m);mkznode(r4, zbrar2, boolvar2, false, m2)) = mkznode(r3, zbrar1, boolvar, true, m1), zh[r2] = mkznode(r4, zbrar2, boolvar2, false, m2), zbrar[n0] = mkzbranch(key0, adr0, r2), zh[zbrar[n].child] = mkznode(r1, zbrar0, boolvar1, false, m0), zh[r] = mkznode(r0, zbrar, false, boolvar0, m), n0 + 1 < # zbrar, n0 < # zbrar, n0 < m, n < # zbrar, n0 < n, r2 ∈ zh, r ∈ zh ⊦ n0 = n

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: r2 = r

Additional information

Used simplifier rules: ⊦ mkznode(r, zbrar, boolvar, boolvar0, m) = mkznode(r0, zbrar0, boolvar1, boolvar2, m0) ↔ r = r0 ∧ zbrar = zbrar0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2) ∧ m = m0; (ws)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic Used formulas: r2 = r