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Proof step 22 from proof btree-sub-clean-write-branches (previous step)

(zbrar[n].child = r ⊃ mkznode(r0, zbrar[n, mkzbranch(key, adr, zbrar[n].child)], false, boolvar0, m);mkznode(r1, zbrar0, boolvar1, false, m0)) = mkznode(r3, zbrar1, boolvar, true, m1), zh[r] = mkznode(r0, zbrar, false, boolvar0, m), zh[zbrar[n].child] = mkznode(r1, zbrar0, boolvar1, false, m0), n < m, n < # zbrar, zbrar[n].child ∈ zh, r ∈ zh ⊦

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: zbrar[n].child = 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: zbrar[n].child = r