Nuprl Lemma : inject_wf

[A,B:Type]. ∀[f:A ⟶ B].  (Inj(A;B;f) ∈ ℙ)


Proof




Definitions occuring in Statement :  inject: Inj(A;B;f) uall: [x:A]. B[x] prop: member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T inject: Inj(A;B;f) so_lambda: λ2x.t[x] implies:  Q prop: so_apply: x[s]
Lemmas referenced :  all_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality functionEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry Error :functionIsType,  Error :universeIsType,  isect_memberEquality Error :inhabitedIsType,  because_Cache universeEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  B].    (Inj(A;B;f)  \mmember{}  \mBbbP{})



Date html generated: 2019_06_20-PM-00_26_22
Last ObjectModification: 2018_09_26-AM-11_48_49

Theory : fun_1


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