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Theorem sub-eq

⊦ i - j = i0 ↔ i = i0 + j

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: abs-01, abs-05, abs-07, abs-08, abs-18, abs-21, abs-add-zero, abs-neg, abs-succ, absa, absls-04, absneg-01, absneg-02, absone-01, add-rew, add-shift, k-sub-rec1, k-sub-rec2, minus-01, minus-02, minus-ass, minus-neg, minus-rew, minus-sub, mone-01, mone-03, neg-06, neg-10, neg-11, neg-12, neg-14, neg-15, negeq, negone, num-eq-shift, num-subadd, numabsneg, numadd, numadd-01, numsub, one-03, rew-eqzero, rew-eqzero-01, sub-add-04, sub-add-05, sub-add-07, sub-add-08, sub-add-09, sub-minus, sub-shift, sub-shift-second, sub-sub, sub-sub-01, sub-sub-02, sub-sub-03, sub-sub-04, sub-zero, sub-zero-01, subsub,
Used by units in proved state: int-mult, int-pot, int-gcd, int-div, intnat, int-square, int-min,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 1
Used lemmas: sub-add, sub-add-01,
Used spec theorems:
- Used simplifier rules:
  - int-basic2/add-c
  - int-basic2/add-a