Nuprl Lemma : eqfun_p_wf
∀[T:Type]. ∀[eq:T ⟶ T ⟶ 𝔹]. (IsEqFun(T;eq) ∈ ℙ)
Proof
Definitions occuring in Statement :
eqfun_p: IsEqFun(T;eq),
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eqfun_p: IsEqFun(T;eq),
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s]
Lemmas referenced :
uall_wf,
uiff_wf,
assert_wf,
equal_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :universeIsType,
Error :inhabitedIsType,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}]. (IsEqFun(T;eq) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_29_12
Last ObjectModification:
2018_09_26-AM-11_46_41
Theory : rel_1
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