### Nuprl Lemma : subgrp_p_wf

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

Proof

Definitions occuring in Statement :  subgrp_p: `s SubGrp of g` grp_car: `|g|` grp_sig: `GrpSig` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  subgrp_p: `s SubGrp of g` uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ` and: `P ∧ Q` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` implies: `P `` Q` so_apply: `x[s]` all: `∀x:A. B[x]` infix_ap: `x f 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

Latex:
\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

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