---

Step * 1 of Lemma funinv-compose


1. n : ℕ
2. f : ℕn ⟶ ℕn
3. Inj(ℕn;ℕn;f)
4. g : ℕn ⟶ ℕn
5. Inj(ℕn;ℕn;g)
6. f o g ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
7. f ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
8. g ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
⊢ inv(f o g) = (inv(g) o inv(f)) ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
BY
{ TACTIC:((InstLemma `funinv_wf2` [⌜n⌝;⌜f o g⌝]⋅ THEN Auto)
          THEN (InstLemma `funinv_wf2` [⌜n⌝;⌜f⌝]⋅ THEN Auto)
          THEN InstLemma `funinv_wf2` [⌜n⌝;⌜g⌝]⋅
          THEN Auto) }

1
1. n : ℕ
2. f : ℕn ⟶ ℕn
3. Inj(ℕn;ℕn;f)
4. g : ℕn ⟶ ℕn
5. Inj(ℕn;ℕn;g)
6. f o g ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
7. f ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
8. g ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
9. inv(f o g) ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
10. inv(f) ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
11. inv(g) ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 
⊢ inv(f o g) = (inv(g) o inv(f)) ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} 

---

Latex:

---

Latex:

1.  n  :  \mBbbN{}
2.  f  :  \mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n
3.  Inj(\mBbbN{}n;\mBbbN{}n;f)
4.  g  :  \mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n
5.  Inj(\mBbbN{}n;\mBbbN{}n;g)
6.  f  o  g  \mmember{}  \{f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;f)\} 
7.  f  \mmember{}  \{f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;f)\} 
8.  g  \mmember{}  \{f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;f)\} 
\mvdash{}  inv(f  o  g)  =  (inv(g)  o  inv(f))


By

---

Latex:
TACTIC:((InstLemma  `funinv\_wf2`  [\mkleeneopen{}n\mkleeneclose{};\mkleeneopen{}f  o  g\mkleeneclose{}]\mcdot{}  THEN  Auto)
                THEN  (InstLemma  `funinv\_wf2`  [\mkleeneopen{}n\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{}]\mcdot{}  THEN  Auto)
                THEN  InstLemma  `funinv\_wf2`  [\mkleeneopen{}n\mkleeneclose{};\mkleeneopen{}g\mkleeneclose{}]\mcdot{}
                THEN  Auto)

---

Home Index