Nuprl Lemma : subgrp_p_wf

[g:GrpSig]. ∀[s:|g| ⟶ ℙ].  (s SubGrp of g ∈ ℙ)


Definitions occuring in Statement :  subgrp_p: SubGrp of g grp_car: |g| grp_sig: GrpSig uall: [x:A]. B[x] prop: member: t ∈ T function: x:A ⟶ B[x]
Definitions unfolded in proof :  subgrp_p: SubGrp of g uall: [x:A]. B[x] member: t ∈ T prop: and: P ∧ Q subtype_rel: A ⊆B so_lambda: λ2x.t[x] implies:  Q so_apply: x[s] all: x:A. B[x] infix_ap: y
Lemmas referenced :  grp_id_wf all_wf grp_car_wf grp_inv_wf infix_ap_wf grp_op_wf grp_sig_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut productEquality applyEquality hypothesisEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis lambdaEquality universeEquality because_Cache functionEquality axiomEquality equalityTransitivity equalitySymmetry cumulativity isect_memberEquality

\mforall{}[g:GrpSig].  \mforall{}[s:|g|  {}\mrightarrow{}  \mBbbP{}].    (s  SubGrp  of  g  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-00_08_49
Last ObjectModification: 2015_12_26-PM-11_45_43

Theory : groups_1

Home Index