### 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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