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Theorem appinf-to-split

⊦ (⌜x⌝ + ⌜nf⌝ ).f to n = (n ≤ # x ⊃ x to n;x + (nf to (n - # x)))

Type: A user defined theorem
Validity: The proof is valid.
Features: ls,
Comment:
Used by: appinf-one-to-succ, appinf-one-to-succ2, appinf-to-ge, appinf-to-ge-01, appinf-to-le,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 9
Used lemmas: get-finto, length-to, append-fininf, get-infto, size-inf-to,
Used spec theorems:
- list-getput/extension
Used simplifier rules: