Nuprl Lemma : comm_wf
∀[T:Type]. ∀[op:T ⟶ T ⟶ T].  (Comm(T;op) ∈ ℙ)
Proof
Definitions occuring in Statement : 
comm: Comm(T;op)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
comm: Comm(T;op)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
infix_ap: x f y
, 
so_apply: x[s]
Lemmas referenced : 
uall_wf, 
equal_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaEquality, 
applyEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
isect_memberEquality, 
because_Cache, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[op:T  {}\mrightarrow{}  T  {}\mrightarrow{}  T].    (Comm(T;op)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_13-PM-04_08_53
Last ObjectModification:
2015_12_26-AM-11_03_08
Theory : fun_1
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