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Proof step 51 from proof program+leftmost (previous step)

∀ t0, r5, r, r0, r3, a, r6, t2, r1, t1, a0, P, H. # t0 < # branch(t3, a2, t4) → ( r5 = r ∧ r0 ≠ null ∧ r ≠ null ∧ (r0 => mknode(r3, a, r6) * tr(r3, t0) * tr(r6, t2) * tr(r1, t1) * r => mknode(r0, a0, r1) * P)(H) → 〈while r3 ≠ null do { r5 := r0 ; r0 := r3 ; r3 := H[r0] .left }〉〈a1 := H[r0] .val ; r3 := H[r0] .right ; H[r5] .left := r3〉 ((tr(r, branch((t0 = leaf ⊃ t2; branch(t0 .butleftmost, a, t2)), a0, t1)) * P * true)(H) ∧ a1 = ((t0 = leaf ⊃ a; t0 .leftmost)))), r5 = r, r0 ≠ null, r ≠ null, (r0 => mknode(r3, a, r6) * tr(r3, branch(t3, a2, t4)) * tr(r6, t2) * tr(r1, t1) * r => mknode(r0, a0, r1) * P)(H), r2 = r0, r4 = r3, r7 = H[r4] .left ⊦ 〈while r7 ≠ null do { r2 := r4 ; r4 := r7 ; r7 := H[r4] .left }〉〈a1 := H[r4] .val ; r7 := H[r4] .right ; H[r2] .left := r7〉 ( (tr(r, branch(branch((t3 = leaf ⊃ t4; branch(t3 .butleftmost, a2, t4)), a, t2), a0, t1)) * P * true)(H) ∧ a1 = ((t3 = leaf ⊃ a2; t3 .leftmost)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
∀ t0, r5, r, r0, r3, a, r6, t2, r1, t1, a0, P, H. # t0 < # branch(t3, a2, t4) → ( r5 = r ∧ r0 ≠ null ∧ r ≠ null ∧ (r0 => mknode(r3, a, r6) * tr(r3, t0) * tr(r6, t2) * tr(r1, t1) * r => mknode(r0, a0, r1) * P)(H) → 〈while r3 ≠ null do { r5 := r0 ; r0 := r3 ; r3 := H[r0] .left }〉〈a1 := H[r0] .val ; r3 := H[r0] .right ; H[r5] .left := r3〉 ((tr(r, branch((t0 = leaf ⊃ t2; branch(t0 .butleftmost, a, t2)), a0, t1)) * P * true)(H) ∧ a1 = ((t0 = leaf ⊃ a; t0 .leftmost)))), r5 = r, r0 ≠ null, r ≠ null, (r0 => mknode(r3, a, r6) * tr(r3, branch(t3, a2, t4)) * tr(r6, t2) * tr(r1, t1) * r => mknode(r0, a0, r1) * P)(H), r2 = r0, r4 = r3, r7 = r8, H[r4] = mknode(r8, a3, r9) ⊦ 〈while r7 ≠ null do { r2 := r4 ; r4 := r7 ; r7 := H[r4] .left }〉〈a1 := H[r4] .val ; r7 := H[r4] .right ; H[r2] .left := r7〉 ( (tr(r, branch(branch((t3 = leaf ⊃ t4; branch(t3 .butleftmost, a2, t4)), a, t2), a0, t1)) * P * true)(H) ∧ a1 = ((t3 = leaf ⊃ a2; t3 .leftmost)))

Rule argument

[x0lemmaarg: spec-name: node instance-name: lemma-name: elim antecedent: succedent: r = nd .left ∧ a = nd .val ∧ r0 = nd .right ↔ nd = mknode(r, a, r0) substlist: [nd, r, a, r0] → [H[r4], r8, a3, r9] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ r = nd .left ∧ a = nd .val ∧ r0 = nd .right ↔ nd = mknode(r, a, r0)])], [EXTRATERMS : (H[r4], r8, a3, r9)]]