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Proof step 3 from proof antisym (previous step)

⊦ ⌜i⌝ = i∞0, ⌜i⌝ < i∞0, i∞0 < ⌜i⌝

User applied rule structural induction

And closed the goal!

Rule argument

indvar: i∞0

Additional information

Used simplifier rules: not-less-neginf: ⊦ ¬ i∞ < -∞;%neginf-less: ⊦ -∞ < i∞ ↔ i∞ ≠ -∞;%less-inf: ⊦ i∞ < ∞ ↔ i∞ ≠ ∞;%less-int: ⊦ ⌜i⌝ < ⌜i0⌝ ↔ i < i0;%intinf freely generated by -∞, ∞, ⌜ ⌝;;%inj: ⊦ ⌜i⌝ = ⌜i0⌝ ↔ i = i0; from specification int-inf-basic%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%lst-02: ⊦ ¬ i < j → (¬ j < i ↔ i = j); from specification int-basic1%disj-02: ⊦ ⌜i⌝ ≠ ∞; from specification int-inf-basic%disj-01: ⊦ ⌜i⌝ ≠ -∞; from specification int-inf-basic