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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