[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 47 from proof pop-corr (previous step)

buf .len = n→i(# x) + 1, a ' + x = tolist(buf, 1 + # x), 0 ≤ buf .first, buf .first < n→i(# buf .data), inv(buf) ⊦ # buf .data = 0, inv(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ inv(buf) ↔ buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ buf .first ∧ buf .first < buf .size ∧ 0 ≤ buf .len ∧ buf .len ≤ buf .size
Proof step 46:
buf .len = n→i(# x) + 1, a ' + x = tolist(buf, 1 + # x), 0 ≤ buf .first, buf .first < n→i(# buf .data), inv(buf) ⊦ # buf .data = 0, (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .size = n→i(# (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .data) ∧ (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .size ≠ 0 ∧ 0 ≤ (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .first ∧ (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .first < (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .size ∧ 0 ≤ (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .len ∧ (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .len ≤ (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) .size

Rule argument

[x0lemmaarg: spec-name: ring-buffer-inv instance-name: lemma-name: inv antecedent: succedent: inv(buf) ↔ buf .size = n→i(# buf .data) ∧ buf .size ≠ 0 ∧ 0 ≤ buf .first ∧ buf .first < buf .size ∧ 0 ≤ buf .len ∧ buf .len ≤ buf .size substlist: [buf] → [ buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : ( buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x))]]