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Proof step 74 from proof push-corr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ abs(buf, x) ↔ buf .len = n→i(# x) ∧ x = tolist(buf, i→n(buf .len))
Proof step 73:
inv(buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)), 0 ≤ (buf .first + buf .len) % buf .size, (buf .first + buf .len) % buf .size < n→i(# buf .data), 0 < buf .size, 0 ≤ buf .len, inv(buf), buf .len < buf .size ⊦ # buf .data = 0, (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .len = n→i(# (tolist(buf, i→n(buf .len)) + a ')) ∧ tolist(buf, i→n(buf .len)) + a ' = tolist (buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len), i→n((buf .data:= (buf .data)[i→n((buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)) .len))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: abs antecedent: succedent: abs(buf, x) ↔ buf .len = n→i(# x) ∧ x = tolist(buf, i→n(buf .len)) substlist: [x, buf] → [tolist(buf, i→n(buf .len)) + a ', buf .data:= (buf .data)[i→n ( (buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len)] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (tolist(buf, i→n(buf .len)) + a ', buf .data:= (buf .data)[i→n ( (buf .first + buf .len) % buf .size), a] .len:= (1 + buf .len))]]