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Proof step 45 from proof path-equiv-reach (previous step)

path(a0 ' + y0 + a '), ¬ path(a0 ' + y0) ∨ (a0 ' + y0) .last ≠ y0 .last ⊦ reach(a0, y0 .last, # y0), ∃ c. reach(a0, c, # y0) ∧ a ∈ succ(c)

User applied rule case distinction

And obtained the following new goals

Proof step 40:
¬ path(a0 ' + y0), path(a0 ' + y0 + a ') ⊦ reach(a0, y0 .last, # y0), ∃ c. reach(a0, c, # y0) ∧ a ∈ succ(c)
Proof step 44:
(a0 ' + y0) .last ≠ y0 .last, path(a0 ' + y0 + a ') ⊦ reach(a0, y0 .last, # y0), ∃ c. reach(a0, c, # y0) ∧ a ∈ succ(c)

Rule argument

[CASEDARG : pos: left 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]