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Proof step 31 from proof program+leftmost (previous step)

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, (_∃ λ r0, r1. r => mknode(r0, a0, r1) * tr(r0, branch((t3 = leaf ⊃ t4; branch(t3 .butleftmost, a2, t4)), a1, t0)) * tr(r1, t1) * P * true)(H1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
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, ∃ r0, r1. ((r => mknode(r0, a0, r1) * tr(r0, branch((t3 = leaf ⊃ t4; branch(t3 .butleftmost, a2, t4)), a1, t0)) * tr(r1, t1)) * true * P)(H1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ P0 * P1 = P1 * P0], [CSIMPSEQ : ⊦ (P0 * P1) * P2 = P0 * P1 * P2], [CSIMPSEQ : ⊦ (_∃ rrP * P)(H) ↔ (∃ r0, r1. (rrP(r0, r1) * P)(H))])]]