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Proof step 7 from proof reach-trans (previous step)

reach(a, b, n), reach(b, c, m) ⊦ reach(a, c, m + n)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ reach(a, b, 0) ↔ a = b
Proof step 6:
∀ a, b, n, c. reach(a, b, n) ∧ reach(b, c, m0) → reach(a, c, m0 + n), reach(a, b, n), reach(b, c, m0 +1) ⊦ reach(a, c, m0 +1 + n)

Rule argument

[VARWITHVARSEQSARG : m, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;], [CSIMPSEQ : ⊦ 0 + m = m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])]]