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Proof step 49 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), ¬ inv(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) ∨ ¬ abs(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x), x) ∨ a ≠ (buf .data)[i→n(buf .first)] ⊦ # buf .data = 0

User applied rule cut formula

And obtained the following new goals

Proof step 33:
inv(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)), buf .len = n→i(# x) + 1, a ' + x = tolist(buf, 1 + # x), 0 ≤ buf .first, buf .first < n→i(# buf .data), inv(buf), ¬ inv(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) ∨ ¬ abs(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x), x) ∨ a ≠ (buf .data)[i→n(buf .first)] ⊦ # buf .data = 0
Proof step 48:
buf .len = n→i(# x) + 1, a ' + x = tolist(buf, 1 + # x), 0 ≤ buf .first, buf .first < n→i(# buf .data), inv(buf), ¬ inv(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) ∨ ¬ abs(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x), x) ∨ a ≠ (buf .data)[i→n(buf .first)] ⊦ inv(buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)), # buf .data = 0

Rule argument

[fma-arg: inv (buf .first:= ((buf .first + 1) % buf .size) .len:= n→i(# x)) ]

Additional information

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