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Proof step 92 from proof onlymod-is-update (previous step)

onlyModified(r, st0, st1), ∀ st1, r, st. # st < # st0 → (onlyModified(r, st, st1) → (∃ fis. st1 = update(r, fis, st) ∧ validFields(r, fis, st))) ⊦ ∃ fis. st1 = update(r, fis, st0) ∧ validFields(r, fis, st0), (rk ∈ st0 → rk ∈ st1) ∧ st0[rk] = st1[rk]

User applied rule cut formula

And obtained the following new goals

Proof step 86:
rk ∈ st0, onlyModified(r, st0, st1), ∀ st1, r, st. # st < # st0 → (onlyModified(r, st, st1) → (∃ fis. st1 = update(r, fis, st) ∧ validFields(r, fis, st))) ⊦ ∃ fis. st1 = update(r, fis, st0) ∧ validFields(r, fis, st0), (rk ∈ st0 → rk ∈ st1) ∧ st0[rk] = st1[rk]
Proof step 91:
onlyModified(r, st0, st1), ∀ st1, r, st. # st < # st0 → (onlyModified(r, st, st1) → (∃ fis. st1 = update(r, fis, st) ∧ validFields(r, fis, st))) ⊦ rk ∈ st0, ∃ fis. st1 = update(r, fis, st0) ∧ validFields(r, fis, st0), (rk ∈ st0 → rk ∈ st1) ∧ st0[rk] = st1[rk]

Rule argument

[fma-arg: rk ∈ st0]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (rk ∈ st0)]]