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Proof step 33 from proof program+leftmost (previous step)

r ≠ null, r0 ≠ null, (r0 => mknode(r2, a1, r5) * tr(r2, (t3 = leaf ⊃ t4; branch(t3 .butleftmost, a2, t4))) * tr(r5, t0) * true * tr(r1, t1) * r => mknode(r0, a0, r1) * P )(H1), H1 ≡ H[r11, H[r11] .left:= r9], ((r3 => mknode(r8, a2, r4) * tr(r8, t3) * tr(r4, t4)) * r => mknode(r0, a0, r1) * tr(r1, t1) * tr(r6, t0) * r0 => mknode(r3, a1, r6) * P)(H), ¬ (tr(r, branch(branch((t3 = leaf ⊃ t4; branch(t3 .butleftmost, a2, t4)), a1, t0), a0, t1)) * P * true)(H1), H[r12] = mknode(r7, a3, r9) ⊦

User applied rule simplifier

And obtained the following new goals

Proof step 32:
H[r12] = mknode(r7, a3, r9), ((r3 => mknode(r8, a2, r4) * tr(r8, t3) * tr(r4, t4)) * r => mknode(r0, a0, r1) * tr(r1, t1) * tr(r6, t0) * r0 => mknode(r3, a1, r6) * P)(H), H1 ≡ H[r11, H[r11] .left:= r9], (r0 => mknode(r2, a1, r5) * tr(r2, (t3 = leaf ⊃ t4; branch(t3 .butleftmost, a2, t4))) * tr(r5, t0) * true * tr(r1, t1) * r => mknode(r0, a0, r1) * P )(H1) ⊦ r = null, r0 = null, (tr(r, branch(branch((t3 = leaf ⊃ t4; branch(t3 .butleftmost, a2, t4)), a1, t0), a0, t1)) * P * true)(H1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]