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Proof step 6 from proof restrict-le2 (previous step)

key1 < key0 ⊦ (key ∈ ri ∧ ¬ key1 < key → ¬ key0 < key) ∧ (key ∈ ri ∧ ¬ key0 < key ∧ ¬ key1 < key → (ri |≤ key0 |≤ key1)[key] = ri[key])

User applied rule cut formula

And obtained the following new goals

Proof step 7:
key1 < key0, key ∈ ri ∧ ¬ key1 < key → ¬ key0 < key ⊦ (key ∈ ri ∧ ¬ key1 < key → ¬ key0 < key) ∧ (key ∈ ri ∧ ¬ key0 < key ∧ ¬ key1 < key → (ri |≤ key0 |≤ key1)[key] = ri[key])

Rule argument

fma: key ∈ ri ∧ ¬ key1 < key → ¬ key0 < key

Additional information

Used simplifier rules: transitivity: ⊦ key < key0 ∧ key0 < key1 → key < key1; (forward) from specification oelem[key-order]%nll: ⊦ ¬ key0 < key ∧ key0 < key1 → key < key1; (forward) from specification oelem[key-order] Used formulas: key ∈ ri ∧ ¬ key1 < key → ¬ key0 < key