[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 51 from proof cyclic-floyd-def (previous step)

reachable-n(H, m, r, r0), reachable-n(H, m * n, r, r1), reachable-n(H, n + m, r, r0), ∀ n0. reachable-n(H, m + n0 * n, r, r0) ⊦ m = 0, n = 0, reachable-n(H, 2 * m * n, r, r1)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 7:
reachable-n(H, n, r, r0), m < n ⊦ ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0)
Proof step 50:
∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, m + n - m, r1, r0), reachable-n(H, m, r, r0), reachable-n(H, m * n, r, r1), reachable-n(H, n + m, r, r0), ∀ n0. reachable-n(H, m + n0 * n, r, r0) ⊦ m = 0, n = 0, reachable-n(H, 2 * m * n, r, r1)

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reach-n-split antecedent: reachable-n(H, n, r, r0), m < n succedent: ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0) substlist: [H, n, r, r0, m] → [H, m + n, r, r0, m] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ m < m + n ↔ n ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1])], [EXTRATERMS : (H, m + n, r, r0, m)]]