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Proof step 57 from proof program+leftmost (previous step)

∀ t0, r5, r, r0, r3, a, r6, t2, r1, t1, a0, P, H. # t0 < # t → ( 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, t) * 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((t = leaf ⊃ t2; branch(t .butleftmost, a, t2)), a0, t1)) * P * true)(H) ∧ a1 = ((t = leaf ⊃ a; t .leftmost)))

User applied rule constructor cut

And obtained the following new goals

Proof step 25:
∀ t0, r5, r, r0, r3, a, r6, t2, r1, t1, a0, P, H. # t0 < # t → ( 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, t) * tr(r6, t2) * tr(r1, t1) * r => mknode(r0, a0, r1) * P)(H), t = leaf ⊦ 〈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((t = leaf ⊃ t2; branch(t .butleftmost, a, t2)), a0, t1)) * P * true)(H) ∧ a1 = ((t = leaf ⊃ a; t .leftmost)))
Proof step 56:
∀ t0, r5, r, r0, r3, a, r6, t2, r1, t1, a0, P, H. # t0 < # t → ( 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, t) * tr(r6, t2) * tr(r1, t1) * r => mknode(r0, a0, r1) * P)(H), t = branch(t3, a2, t4) ⊦ 〈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((t = leaf ⊃ t2; branch(t .butleftmost, a, t2)), a0, t1)) * P * true)(H) ∧ a1 = ((t = leaf ⊃ a; t .leftmost)))

Rule argument

[var-arg: t]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : tree generated by leaf, branch;])]]