[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 23 from proof arr2list-put (previous step)

m0 + 1 < # ar, n ≤ m0 + 1, n < # ar, n < # arr2list(ar, m0), ∀ n, ar, bv. n < # ar ∧ n ≤ m0 ∧ m0 < # ar → (arr2list(ar, m0)[n, bv]) = arr2list(ar[n, bv], m0) ⊦ (arr2list(ar, m0)[n, bv]) + ar[m0 + 1] ' = arr2list(ar[n, bv], m0) + (ar[n, bv][m0 + 1]) ', arr2list(ar, m0) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ m ≠ n → (ar[n, bv][m] ↔ ar[m])
Proof step 20:
¬ m0 + 1 ≠ n, m0 + 1 < # ar, n ≤ m0 + 1, n < # ar, n < # arr2list(ar, m0), ∀ n, ar, bv. n < # ar ∧ n ≤ m0 ∧ m0 < # ar → (arr2list(ar, m0)[n, bv]) = arr2list(ar[n, bv], m0) ⊦ (arr2list(ar, m0)[n, bv]) + ar[m0 + 1] ' = arr2list(ar[n, bv], m0) + (ar[n, bv][m0 + 1]) ', arr2list(ar, m0) = []
Proof step 22:
m0 + 1 ≠ n, m0 + 1 < # ar, n ≤ m0 + 1, n < # ar, n < # arr2list(ar, m0), ∀ n, ar, bv. n < # ar ∧ n ≤ m0 ∧ m0 < # ar → (arr2list(ar, m0)[n, bv]) = arr2list(ar[n, bv], m0) ⊦ (arr2list(ar, m0)[n, bv]) + ar[m0 + 1] ' = arr2list(ar[n, bv], m0) + ar[m0 + 1] ', arr2list(ar, m0) = []

Rule argument

[x0lemmaarg: spec-name: array instance-name: boolarr lemma-name: Put-other antecedent: succedent: m ≠ n → (ar[n, bv][m] ↔ ar[m]) substlist: [m, bv, n, ar] → [m0 + 1, bv, n, ar] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 1, 1, 1, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (m0 + 1, bv, n, ar)]]