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Proof step 31 from proof path-equiv-reach (previous step)

y = y1 + a0 ', (a ' + y0) .last = y1 .last, # y = 1 + # y0, reach(a, y1 .last, # y0), path(a ' + y), path(a ' + y0) ⊦ y = [], ∃ c. reach(a, c, # y0) ∧ a0 ∈ succ(c)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
(a ' + y0) .last = y1 .last, # y1 = # y0, reach(a, y1 .last, # y0), path(a ' + y1 + a0 '), path(a ' + y0) ⊦ ∃ c. reach(a, c, # y0) ∧ a0 ∈ succ(c)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ x + a ' ≠ []], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ # a ' = 0 +1], [CSIMPSEQ : ⊦ # (x + y) = # x + # y])]]