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Proof step 42 from proof challenge3 (previous step)

(r => mknode(r1, a, r2) * tr(r1, t0) * tr(r2, t1) * P)(H), bst(t1), bst(t0), (true * tr(r0, branch(t0 .butleftmost, a, t1)) * P)(H0), b ∈ t0, b < t0 .leftmost, ∀ a0. ¬ a0 ∈ t0 ∨ ¬ a0 ∈ t1, ∀ a, c. a ∈ t0 ∧ c ∈ t1 → a < c, ∀ a0. a0 ∈ t1 → a < a0, ∀ a0. a0 ∈ t0 → a0 < a ⊦ r = null, t0 = leaf, b = t0 .leftmost

User applied rule insert lemma

And obtained the following new goals

Proof step 41:
⊦ t ≠ leaf ∧ bst(t) ∧ b ≠ t .leftmost ∧ b ∈ t → t .leftmost < b

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: ismin antecedent: succedent: t ≠ leaf ∧ bst(t) ∧ b ≠ t .leftmost ∧ b ∈ t → t .leftmost < b substlist: [t, b] → [t0, b] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (P0 * P1) * P2 = P0 * P1 * P2], [CSIMPSEQ : ⊦ P0 * P1 = P1 * P0], [CSIMPFORWARD : ⊦ a < b ∧ b < c → a < c], [CSIMPSEQ : ⊦ ¬ a < a])], [EXTRATERMS : (t0, b)]]