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Theorem elim-sub

n ≤ m ⊦ n0 = m - n ↔ m = n0 + n

Type: A user defined theorem
Validity: The proof is valid.
Features: elim,
Comment:
Used by: cancel-01, eq-01, eq-02, l-num-01, l-num-02, le, le-num-01, less, less-02, less-03, ls, ls-01, ls-02, ls-03, ls-04, ls-07, prop-01, prop-02, prop-05, sub-add-01, sub-le-rew, sub-ls, sub-ls-rew, sub-same, succ-05, zero, zero-01,
Used by units in proved state: list-last, list-del, stream, list, nat-pair, nat-div, set-union, stut-mon, path-reachable, nat-prime, nat-inf, nat-even, mon-lim-filter-count, intnat, bag-union, nat-mult, array-copy, streamseq-mon-lim, inf-app-list, infinite-append,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 7
Used lemmas: elim-pred-c, num-01, shift-01, num-02, lels-01, succ-01, sub-base,
Used spec theorems:
- Used simplifier rules: