[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 130 from proof BFS-correct-if-reachable (previous step)

m0 + 1 = n - n0, m1 + 1 = # S0, n0 < n, reach(source, dest, n), INV(S0, S, S1, n0, source), dest ∈ S0, a ∈ S0 ∧ reach(a, dest, n - n0) ∧ ¬ reach<(a, dest, n - n0) ∨ n0 < n ∧ b ∈ S ∧ reach(b, dest, n - n0 - 1) ∧ ¬ reach<(b, dest, n - n0 - 1) ⊦ S0 = ∅, n0 = n, reach<(source, dest, n)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 129:
n = n1 + n0 ∧ n0 ≤ n, m0 + 1 = n1, m1 + 1 = # S0, n0 < n, reach(source, dest, n), INV(S0, S, S1, n0, source), dest ∈ S0, a ∈ S0 ∧ reach(a, dest, n1) ∧ ¬ reach<(a, dest, n1) ∨ n0 < n ∧ b ∈ S ∧ reach(b, dest, n1 - 1) ∧ ¬ reach<(b, dest, n1 - 1) ⊦ S0 = ∅, n0 = n, reach<(source, dest, n)

Rule argument

[x0lemmaarg: spec-name: nat instance-name: lemma-name: elim-sub antecedent: n ≤ m succedent: n0 = m - n ↔ m = n0 + n substlist: [m, n, n0] → [n, n0, n1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m < n → ¬ n < m], [CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (n, n0, n1)]]