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Theorem ext-rec

⊦ cu1 = cu0[nx, ny, nz := a] ↔ #x cu0 = #x cu1 ∧ #y cu0 = #y cu1 ∧ #z cu0 = #z cu1 ∧ (∀ nx0, ny0, nz0. nx0 < #x cu0 ∧ ny0 < #y cu0 ∧ nz0 < #z cu0 → cu1[nx0, ny0, nz0] = (nx = nx0 ∧ ny = ny0 ∧ nz = nz0 ⊃ a;cu0[nx0, ny0, nz0]))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 27
Used lemmas: put-otherheight, put-otherdepth, put-otherwidth, put-same, height-put, depth-put, width-put, extension,
Used spec theorems:
- Used simplifier rules:
  - nat-basic/f
  - nat-basic/lf-01