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Proof step 16 from proof path-equiv-reach (previous step)

path(a ' + y), b ∈ succ(y .last), reach(a, y .last, # y) ⊦ y = [], succ(y .last) = ∅, # succ(y .last) = 0, path(a ' + y + b ')

User applied rule insert lemma

And obtained the following new goals

Proof step 15:
⊦ path(x + a ' + b ') ↔ b ∈ succ(a) ∧ path(x + a ')

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: path-rec antecedent: succedent: path(x + a ' + b ') ↔ b ∈ succ(a) ∧ path(x + a ') substlist: [x, a, b] → [a + y .butlast, y .last, b] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ a + x = a ' + x], [CSIMPSEQ : x ≠ [] ⊦ x .butlast + x .last ' = x])], [EXTRATERMS : (a + y .butlast, y .last, b)]]