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Proof step 12 from proof tr-fold (previous step)

True(H[r] = mknode(r0, a, r1)), (_∃ λ r0, r1. r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P)(H) ⊦ (r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P)(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
((r => mknode(r2, a, r3) * tr(r2, t0) * tr(r3, t1)) * P)(H), True(mknode(r2, a, r3) = mknode(r0, a, r1)) ⊦ (r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P)(H)

Rule argument

[emptyarg]

Additional information

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